The Limiting Behavior of a One-Dimensional Random Walk in a Random Medium

Previous article Next article The Limiting Behavior of a One-Dimensional Random Walk in a Random MediumYa. G. SinaiYa. G. Sinaihttps: //doi. org/10. 1137/1127028PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout1 H. Kesten, , M. W. Koslow and, F. Spitzer, A limit law for random walk in a random environment, Compositio Math. , 30 (1975), 145–168 52: 1895 0388. 60069 Google Scholar2 Fred Solomon, Random walks in a random environment, Ann. Probability, 3 (1975), 1–31 50: 14943 0305. 60029 CrossrefGoogle Scholar3 G. Ritter, Masters Thesis, Random walks in a random environment, critical case, thesis, Cornell University, lthaca, NY, 1976 Google Scholar4 R. A. Minlös and, A. M. Khalfina, A two-dimensional limit theorem for the number of particles and the energy in the grand canonical ensemble, Izv. Akad. Nauk SSSR Ser. Mat. , 34 (1970), 1173–1191, (In Russian. ) 42: 8847 Google Scholar5 V. V. Petrov, Sums of independent random variables, Springer-Verlag, New York, 1975x+346 52: 9335 CrossrefGoogle Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails On the mean square displacement of intruders in freely cooling granular gasesGranular Matter, Vol. 24, No. 4 | 12 September 2022 Cross Ref A study of distributed‐order time fractional diffusion models with continuous distribution weight functionsNumerical Methods for Partial Differential Equations, Vol. 152 | 5 July 2022 Cross Ref Transport and localization in quantum walks on a random hierarchy of barriersJournal of Physics A: Mathematical and Theoretical, Vol. 55, No. 26 | 6 June 2022 Cross Ref Local equilibrium properties of ultraslow diffusion in the Sinai modelNew Journal of Physics, Vol. 24, No. 7 | 19 July 2022 Cross Ref Unravelling the origins of anomalous diffusion: From molecules to migrating storksPhysical Review Research, Vol. 4, No. 3 | 18 July 2022 Cross Ref Emergence of Sinai physics in the stochastic motion of passive and active particlesNew Journal of Physics, Vol. 24, No. 6 | 21 June 2022 Cross Ref Blowup for semilinear fractional diffusion system with Caputo–Hadamard derivativeMathematical Methods in the Applied Sciences, Vol. 38 | 27 May 2022 Cross Ref The killed Brox diffusionStochastic Models, Vol. 24 | 26 May 2022 Cross Ref Computation of the inverse Mittag–Leffler function and its application to modeling ultraslow dynamicsFractional Calculus and Applied Analysis, Vol. 25, No. 2 | 25 April 2022 Cross Ref Theory and experiments for disordered elastic manifolds, depinning, avalanches, and sandpilesReports on Progress in Physics, Vol. 85, No. 8 | 9 August 2022 Cross Ref Broadband NMR relaxometry of electrolytes for energy storageChemical Physics Reviews, Vol. 3, No. 1 | 1 Mar 2022 Cross Ref Translocation, Rejection and Trapping of PolyampholytesPolymers, Vol. 14, No. 4 | 18 February 2022 Cross Ref Non-exponential relaxation models of signal decay in magnetic resonance imagingCommunications in Nonlinear Science and Numerical Simulation, Vol. 102 | 1 Nov 2021 Cross Ref Harry Kesten's work in probability theoryProbability Theory and Related Fields, Vol. 181, No. 1-3 | 25 August 2021 Cross Ref Relations between anomalous diffusion and fluctuation scaling: the case of ultraslow diffusion and time-scale-independent fluctuation scaling in languageThe European Physical Journal B, Vol. 94, No. 11 | 20 November 2021 Cross Ref Backbone diffusion and first-passage dynamics in a comb structure with confining branches under stochastic resettingJournal of Physics A: Mathematical and Theoretical, Vol. 54, No. 40 | 14 September 2021 Cross Ref Emergent hydrodynamics in a strongly interacting dipolar spin ensembleNature, Vol. 597, No. 7874 | 1 September 2021 Cross Ref Fingerprints of viscoelastic subdiffusion in random environments: Revisiting some experimental data and their interpretationsPhysical Review E, Vol. 104, No. 3 | 20 September 2021 Cross Ref Universal excursion and bridge shapes in ABBM/CIR/Bessel processesJournal of Statistical Mechanics: Theory and Experiment, Vol. 2021, No. 8 | 20 August 2021 Cross Ref Bounded weak solutions of time-fractional porous medium type and more general nonlinear and degenerate evolutionary integro-differential equationsJournal of Mathematical Analysis and Applications, Vol. 499, No. 1 | 1 Jul 2021 Cross Ref Matrix Kesten recursion, inverse-Wishart ensemble and fermions in a Morse potentialJournal of Physics A: Mathematical and Theoretical, Vol. 54, No. 25 | 31 May 2021 Cross Ref Hadamard-Type Fractional Heat Equations and Ultra-Slow DiffusionsFractal and Fractional, Vol. 5, No. 2 | 23 May 2021 Cross Ref Probing the topological Anderson transition with quantum walksPhysical Review Research, Vol. 3, No. 2 | 4 June 2021 Cross Ref Constructive approach to limit theorems for recurrent diffusive random walks on a stripAsymptotic Analysis, Vol. 122, No. 3-4 | 7 Apr 2021 Cross Ref Globular Polyampholytes: Structure and TranslocationMacromolecules, Vol. 54, No. 5 | 23 February 2021 Cross Ref A mini-review of the diffusion dynamics of DNA-binding proteins: experiments and modelsJournal of the Korean Physical Society, Vol. 78, No. 5 | 29 January 2021 Cross Ref Applications of Distributed-Order Fractional Operators: A ReviewEntropy, Vol. 23, No. 1 | 15 January 2021 Cross Ref Conduction and Diffusion in Percolating SystemsComplex Media and Percolation Theory | 24 August 2021 Cross Ref Modeling and pricing with a random walk in random environmentInternational Journal of Financial Engineering, Vol. 07, No. 04 | 12 December 2020 Cross Ref Finite-range viscoelastic subdiffusion in disordered systems with inclusion of inertial effectsNew Journal of Physics, Vol. 22, No. 11 | 17 November 2020 Cross Ref Derivation and numerical validation of the fundamental solutions for constant and variable-order structural derivative advection–dispersion modelsZeitschrift für angewandte Mathematik und Physik, Vol. 71, No. 4 | 22 July 2020 Cross Ref Random walks in a strongly sparse random environmentStochastic Processes and their Applications, Vol. 130, No. 7 | 1 Jul 2020 Cross Ref Negative mobility, sliding, and delocalization for stochastic networksPhysical Review E, Vol. 101, No. 6 | 17 June 2020 Cross Ref Fine mesh limit of the VRJP in dimension one and Bass–Burdzy flowProbability Theory and Related Fields, Vol. 177, No. 1-2 | 25 September 2019 Cross Ref Log-periodicity can appear in a non-Markovian random walk even if there is perfect memory of its historyEPL (Europhysics Letters), Vol. 130, No. 2 | 28 May 2020 Cross Ref Tracer diffusion on a crowded random Manhattan latticeNew Journal of Physics, Vol. 22, No. 3 | 23 March 2020 Cross Ref Limit Shape of Minimal Difference Partitions and Fractional StatisticsCommunications in Mathematical Physics, Vol. 373, No. 3 | 25 July 2019 Cross Ref The heavy range of randomly biased walks on treesStochastic Processes and their Applications, Vol. 130, No. 2 | 1 Feb 2020 Cross Ref Crossover Dynamics from Superdiffusion to Subdiffusion: Models and SolutionsFractional Calculus and Applied Analysis, Vol. 23, No. 1 | 27 February 2020 Cross Ref Conduction and Diffusion in Percolating SystemsEncyclopedia of Complexity and Systems Science | 4 December 2020 Cross Ref Recurrence of direct products of diffusion processes in random media having zero potentialsElectronic Journal of Probability, Vol. 25, No. none | 1 Jan 2020 Cross Ref Diffusion Across Semi-permeable Barriers: Spectral Properties, Efficient Computation, and ApplicationsJournal of Scientific Computing, Vol. 81, No. 3 | 26 September 2019 Cross Ref Ramifications of disorder on active particles in one dimensionPhysical Review E, Vol. 100, No. 5 | 21 November 2019 Cross Ref The influences of correlated spatially random perturbations on first passage time in a linear-cubic potentialChaos: An Interdisciplinary Journal of Nonlinear Science, Vol. 29, No. 10 | 1 Oct 2019 Cross Ref Two alternating direction implicit spectral methods for two-dimensional distributed-order differential equationNumerical Algorithms, Vol. 82, No. 1 | 27 September 2018 Cross Ref A Survey of Models of Ultraslow Diffusion in Heterogeneous MaterialsApplied Mechanics Reviews, Vol. 71, No. 4 | 9 July 2019 Cross Ref Invariant measure for random walks on ergodic environments on a stripThe Annals of Probability, Vol. 47, No. 4 | 1 Jul 2019 Cross Ref On properties of the Wang–Landau algorithmJournal of Physics: Conference Series, Vol. 1252, No. 1 | 1 Jun 2019 Cross Ref Distributed order Hausdorff derivative diffusion model to characterize non-Fickian diffusion in porous mediaCommunications in Nonlinear Science and Numerical Simulation, Vol. 70 | 1 May 2019 Cross Ref Quenched central limit theorem rates of convergence for one-dimensional random walks in random environmentsBernoulli, Vol. 25, No. 2 | 1 May 2019 Cross Ref Berry–Esseen estimates for regenerative processes under weak moment assumptionsStochastic Processes and their Applications, Vol. 129, No. 4 | 1 Apr 2019 Cross Ref Statistical mechanics of a single active slider on a fluctuating interfacePhysical Review E, Vol. 99, No. 4 | 17 April 2019 Cross Ref Quantifying brain microstructure with diffusion MRI: Theory and parameter estimationNMR in Biomedicine, Vol. 32, No. 4 | 15 October 2018 Cross Ref A block-centred finite difference method for the distributed-order differential equation with Neumann boundary conditionInternational Journal of Computer Mathematics, Vol. 96, No. 3 | 8 May 2018 Cross Ref Anomalously Slow Dewetting of Colloidal Particles at a Liquid/Gas InterfaceColloids and Interfaces, Vol. 3, No. 1 | 8 February 2019 Cross Ref Two-Boundary Problem for a Random Walk in a Random EnvironmentV. I. AfanasyevTheory of Probability & Its Applications, Vol. 63, No. 3 | 5 February 2019AbstractPDF (172 KB) Random Walks in Cooling Random EnvironmentsSojourns in Probability Theory and Statistical Physics - III | 18 October 2019 Cross Ref Mathematical PhysicsThe Abel Prize 2013-2017 | 24 February 2019 Cross Ref Density Estimation for RWREMathematical Methods of Statistics, Vol. 28, No. 1 | 3 May 2019 Cross Ref Random walk in cooling random environment: ergodic limits and concentration inequalitiesElectronic Journal of Probability, Vol. 24, No. none | 1 Jan 2019 Cross Ref Arbitrary many walkers meet infinitely often in a subballistic random environmentElectronic Journal of Probability, Vol. 24, No. none | 1 Jan 2019 Cross Ref Two temporal second-order H1-Galerkin mixed finite element schemes for distributed-order fractional sub-diffusion equationsNumerical Algorithms, Vol. 79, No. 4 | 25 January 2018 Cross Ref Numerical algorithms for multidimensional time-fractional wave equation of distributed-order with a nonlinear source termAdvances in Difference Equations, Vol. 2018, No. 1 | 3 October 2018 Cross Ref Clustering, intermittency, and scaling for passive particles on fluctuating surfacesPhysical Review E, Vol. 98, No. 5 | 30 November 2018 Cross Ref Scaling limit theorem for transient random walk in random environmentFrontiers of Mathematics in China, Vol. 13, No. 5 | 3 September 2018 Cross Ref A block-centered finite difference method for the distributed-order time-fractional diffusion-wave equationApplied Numerical Mathematics, Vol. 131 | 1 Sep 2018 Cross Ref Central limit theorem for recurrent random walks on a strip with bounded potentialNonlinearity, Vol. 31, No. 7 | 6 June 2018 Cross Ref Localization due to topological stochastic disorder in active networksPhysical Review E, Vol. 98, No. 1 | 5 July 2018 Cross Ref Empirical observations of ultraslow diffusion driven by the fractional dynamics in languagesPhysical Review E, Vol. 98, No. 1 | 18 July 2018 Cross Ref Cold Active Motion: How Time-Independent Disorder Affects the Motion of Self-Propelled AgentsPhysical Review Letters, Vol. 120, No. 23 | 6 June 2018 Cross Ref Translocation of polyampholytes and intrinsically disordered proteins⋆The European Physical Journal E, Vol. 41, No. 6 | 21 June 2018 Cross Ref Replica symmetry breaking in trajectory space for diffusion in logarithmically correlated random potentialsJournal of Statistical Mechanics: Theory and Experiment, Vol. 2018, No. 5 | 16 May 2018 Cross Ref Continuous time random walk model with asymptotical probability density of waiting times via inverse Mittag-Leffler functionCommunications in Nonlinear Science and Numerical Simulation, Vol. 57 | 1 Apr 2018 Cross Ref Response to a small external force and fluctuations of a passive particle in a one-dimensional diffusive environmentPhysical Review E, Vol. 97, No. 4 | 11 April 2018 Cross Ref A non-local structural derivative model for characterization of ultraslow diffusion in dense colloidsCommunications in Nonlinear Science and Numerical Simulation, Vol. 56 | 1 Mar 2018 Cross Ref A real distinct poles rational approximation of generalized Mittag-Leffler functions and their inverses: Applications to fractional calculusJournal of Computational and Applied Mathematics, Vol. 330 | 1 Mar 2018 Cross Ref Range and critical generations of a random walk on Galton–Watson treesAnnales de l'Institut Henri Poincaré, Probabilités et Statistiques, Vol. 54, No. 1 | 1 Feb 2018 Cross Ref Diffusion entropy method for ultraslow diffusion using inverse Mittag-Leffler functionFractional Calculus and Applied Analysis, Vol. 21, No. 1 | 13 March 2018 Cross Ref From continuous time random walks to the generalized diffusion equationFractional Calculus and Applied Analysis, Vol. 21, No. 1 | 13 March 2018 Cross Ref Quantum Lattice Boltzmann Study of Random-Mass Dirac Fermions in One DimensionMany-body Approaches at Different Scales | 25 March 2018 Cross Ref Двуграничная задача для случайного блуждания в случайной средеТеория вероятностей и ее применения, Vol. 63, No. 3 | 1 Jan 2018 Cross Ref Dynamical freezing in a spin glass system with logarithmic correlationsElectronic Journal of Probability, Vol. 23, No. none | 1 Jan 2018 Cross Ref Subdiffusion via dynamical localization induced by thermal equilibrium fluctuationsScientific Reports, Vol. 7, No. 1 | 28 November 2017 Cross Ref Narrow log-periodic modulations in non-Markovian random walksPhysical Review E, Vol. 96, No. 6 | 26 December 2017 Cross Ref Persistent Sinai-type diffusion in Gaussian random potentials with decaying spatial correlationsPhysical Review E, Vol. 96, No. 5 | 22 November 2017 Cross Ref Ageing effects in ultraslow continuous time random walksThe European Physical Journal B, Vol. 90, No. 11 | 1 November 2017 Cross Ref Hydrodynamic limit for a system of independent, sub-ballistic random walks in a common random environmentAnnales de l'Institut Henri Poincaré, Probabilités et Statistiques, Vol. 53, No. 4 | 1 Nov 2017 Cross Ref Nonstationary Markovian replication process causing diverse diffusionsPhysical Review E, Vol. 96, No. 4 | 19 October 2017 Cross Ref A generalization of the Lomnitz logarithmic creep law via Hadamard fractional calculusChaos, Solitons & Fractals, Vol. 102 | 1 Sep 2017 Cross Ref New methodologies in fractional and fractal derivatives modelingChaos, Solitons & Fractals, Vol. 102 | 1 Sep 2017 Cross Ref Beyond monofractional kineticsChaos, Solitons & Fractals, Vol. 102 | 1 Sep 2017 Cross Ref Heat conduction and the nonequilibrium stationary states of stochastic energy exchange processesJournal of Statistical Mechanics: Theory and Experiment, Vol. 2017, No. 8 | 22 August 2017 Cross Ref Diffusion in time-dependent random media and the Kardar-Parisi-Zhang equationPhysical Review E, Vol. 96, No. 1 | 10 July 2017 Cross Ref Fractional diffusion equation with distributed-order material derivative. Stochastic foundationsJournal of Physics A: Mathematical and Theoretical, Vol. 50, No. 18 | 5 April 2017 Cross Ref Out-of-time-order correlation in marginal many-body localized systemsPhysical Review B, Vol. 95, No. 16 | 24 April 2017 Cross Ref Ultraslow diffusion and weak ergodicity breaking in right triangular billiardsPhysical Review E, Vol. 95, No. 3 | 10 March 2017 Cross Ref Random Walks and Branching Processes in Correlated Gaussian EnvironmentJournal of Statistical Physics, Vol. 166, No. 1 | 24 November 2016 Cross Ref Aging underdamped scaled Brownian motion: Ensemble- and time-averaged particle displacements, nonergodicity, and the failure of the overdamping approximationPhysical Review E, Vol. 95, No. 1 | 12 January 2017 Cross Ref Asymptotic direction for random walks in mixing random environmentsElectronic Journal of Probability, Vol. 22, No. none | 1 Jan 2017 Cross Ref Decay estimates for time-fractional and other non-local in time subdiffusion equations in Rᵈ R dMathematische Annalen, Vol. 366, No. 3-4 | 5 January 2016 Cross Ref Quasi-Many-Body Localization in Translation-Invariant SystemsPhysical Review Letters, Vol. 117, No. 24 | 7 December 2016 Cross Ref Finite current stationary states of random walks on one-dimensional lattices with aperiodic disorderPhysica A: Statistical Mechanics and its Applications, Vol. 461 | 1 Nov 2016 Cross Ref Sinai Diffusion at Quasi-1D Topological Phase TransitionsPhysical Review Letters, Vol. 117, No. 19 | 1 November 2016 Cross Ref StructuRal Derivative Based on Inverse Mittag-Leffler Function for Modeling Ultraslow DiffusionFractional Calculus and Applied Analysis, Vol. 19, No. 5 | 5 November 2016 Cross Ref Lévy processes on a generalized fractal combJournal of Physics A: Mathematical and Theoretical, Vol. 49, No. 35 | 22 July 2016 Cross Ref Percolation, sliding, localization and relaxation in topologically closed circuitsScientific Reports, Vol. 6, No. 1 | 10 March 2016 Cross Ref Underdamped scaled Brownian motion: (non-) existence of the overdamped limit in anomalous diffusionScientific Reports, Vol. 6, No. 1 | 27 July 2016 Cross Ref Sample-to-sample fluctuations of power spectrum of a random motion in a periodic Sinai modelPhysical Review E, Vol. 94, No. 3 | 26 September 2016 Cross Ref Persistence of some additive functionals of Sinai's walkAnnales de l'Institut Henri Poincaré, Probabilités et Statistiques, Vol. 52, No. 3 | 1 Aug 2016 Cross Ref On the approximate controllability for fractional evolution hemivariational inequalitiesMathematical Methods in the Applied Sciences, Vol. 39, No. 11 | 26 October 2015 Cross Ref Relaxation rate of a stochastic spreading process in a closed ringPhysical Review E, Vol. 93, No. 6 | 29 June 2016 Cross Ref The Quenched Critical Point for Self-Avoiding Walk on Random ConductorsJournal of Statistical Physics, Vol. 163, No. 4 | 30 March 2016 Cross Ref A comparison of random walks in dependent random environmentsAdvances in Applied Probability, Vol. 48, No. 1 | 24 March 2016 Cross Ref Suppression of thermal noise in a non-Markovian random velocity fieldJournal of Statistical Mechanics: Theory and Experiment, Vol. 2016, No. 2 | 25 February 2016 Cross Ref Random field disorder at an absorbing state transition in one and two dimensionsPhysical Review E, Vol. 93, No. 2 | 16 February 2016 Cross Ref Elastic Interfaces Driven in Interfaces Driven in Media | 10 July 2015 Cross Ref with Slow and Ultraslow of Vol. No. 3 | 21 June 2016 Cross Ref Random walks in a sparse random environmentElectronic Journal of Probability, Vol. 21, No. none | 1 Jan 2016 Cross Ref Scaling limit of time of Sinai's random of Mathematics in China, Vol. No. 6 | 13 August 2015 Cross Ref Recurrence of the Brownian Motion in and Gaussian Analysis, Vol. No. 4 | 7 July 2015 Cross Ref Recurrence of diffusion processes in Brownian Systems and Differential Equations, 2015 of the Conference | 1 Nov 2015 Cross Ref difference for distributed-order time-fractional diffusion-wave equation on bounded of Computational Physics, Vol. | 1 Oct 2015 Cross Ref dynamics in using NMR relaxometry and Vol. 70 | 1 Sep 2015 Cross Ref of for transient random walks in random of Mathematics in China, Vol. No. 4 | 25 June 2015 Cross Ref Ageing first passage time density in continuous time random walks and energy of Physics A: Mathematical and Theoretical, Vol. 48, No. 28 | 18 June 2015 Cross Ref of to Sinai on of Statistical Physics, Vol. No. 2 | 30 April 2015 Cross Ref Ultraslow scaled Brownian Journal of Physics, Vol. No. 6 | 29 June 2015 Cross Ref diffusion of Brownian particles on disordered correlated potentialsJournal of Statistical Mechanics: Theory and Experiment, Vol. No. 6 | 3 June 2015 Cross Ref and of random quantum properties of the energy at of Statistical Mechanics: Theory and Experiment, Vol. No. 6 | 30 June 2015 Cross Ref and of Brownian in a model of Review E, Vol. No. 5 | 21 May 2015 Cross Ref in Vol. No. 3 | 1 Apr 2015 Cross Ref Decay for and Subdiffusion Equations via and Journal on Mathematical Analysis, Vol. 47, No. 1 | 8 January Numerical Methods for the Distributed-Order in Mathematical Physics, Vol. 2015 | 1 Jan 2015 Cross Ref and fluctuations in ultraslow diffusion processesJournal of Physics A: Mathematical and Theoretical, Vol. 47, No. | 14 November Cross Ref and of the dynamics in disordered interacting many-body and ultraslow Journal of Physics, Vol. No. 11 | 24 November Cross Ref The Abel Prize to Mathematical Vol. No. 5 | 20 January 2015 Cross Ref for Processes in Random | 29 September Cross Ref Diffusion in correlated random of Physics A: Mathematical and Theoretical, Vol. 47, No. | 29 August Cross Ref diffusion in disordered at a finite Review E, Vol. 90, No. 3 | 3 September Cross Ref of the Review E, Vol. 90, No. 3 | 22 September Cross Ref Scaling of stationary probability of random walks on one-dimensional lattices with aperiodic Review E, Vol. No. 6 | 4 June Cross Ref Ultraslow diffusion in an non-Markovian random Review E, Vol. No. 5 | 8 May Cross Ref of in a model with heavy Review E, Vol. No. 4 | 4 April Cross Ref in Random Walks in Random in and Systems | 17 June Cross Ref Transport and in and Systems | 20 October Cross Ref Conduction and Diffusion in Percolating SystemsEncyclopedia of Complexity and Systems Science | 26 December Cross Ref diffusion models and their and at the of single particle Vol. No. | 1 January Cross Ref Vol. No. | 1 Jan Cross Ref random walksPhysical Review E, Vol. No. 6 | 5 December Cross Ref of distributed-order fractional diffusion on and Applied Analysis, Vol. 13, No. 2 | 1 Oct Cross Ref one-dimensional Anderson localization and products of random of Physics A: Mathematical and Theoretical, Vol. No. 25 | 4 June Cross Ref Persistence and first-passage properties in nonequilibrium in Physics, Vol. No. 3 | 1 Jun Cross Ref Limit theorems for random walks on a strip in Vol. No. 6 | 20 May Cross Ref Dynamical of and random models on fractal of Statistical Mechanics: Theory and Experiment, Vol. No. | 14 June Cross Ref Quenched limits for the fluctuations of transient random walks in random on Annals of Applied Probability, Vol. 23, No. 3 | 1 Jun Cross Ref Dynamical for the random model on the of the real space of Statistical Mechanics: Theory and Experiment, Vol. No. | 17 May Cross Ref of in Random with Correlated Review Letters, Vol. No. 10 | 8 March Cross Ref Dynamics of models zero of Statistical Mechanics: Theory and Experiment, Vol. No. | 25 February Cross Ref process with Review E, Vol. No. 2 | 21 February Cross Ref Localization for a Random Walk in Random of Statistical Physics, Vol. No. 2 | 15 December Cross Ref and in diffusion Physics, Vol. No. | 1 Jan Cross Ref convergence for biased random walks on Theory and Related Fields, Vol. No. 3-4 | 8 July Cross Ref breaking for the modelPhysical Review E, Vol. No. 4 | 19 October Cross Ref Random at a Phase Review Letters, Vol. No. 17 | 26 October Cross Ref Two at the Vol. No. 9 | 1 Sep Cross Ref for in R of | 15 January Cross Ref and in Random Walks in Random Phase and of Statistical Physics, Vol. No. 6 | 6 June Cross Ref The of disorder on the diffusion in (Europhysics Letters), Vol. 98, No. 3 | 4 May Cross Ref entropy dynamics of disordered quantum spin Review B, Vol. 85, No. 9 | 12 March Cross Ref estimates of the diffusion of a single Brownian Review E, Vol. 85, No. 3 | 22 March Cross Ref Random Walks in Random Complexity | 1 Jan Cross Ref between disorder and A numerical study of Review E, Vol. 85, No. 1 | 11 January Cross Ref On the of and of Physics A: Mathematical and Theoretical, Vol. No. | 21 September Cross Ref On the of anomalous and ultraslow of Physics A: Mathematical and Theoretical, Vol. No. 40 | 15 September Cross Ref for the time of a diffusion in Brownian environmentStochastic Processes and their Applications, Vol. No. 10 | 1 Oct Cross Ref of A Conference on and | 1 Oct Cross Ref Limit of the Local for of Probability, Vol. 24, No. 3 | 6 October Cross Ref fractional on bounded of Mathematical Analysis and Applications, Vol. No. 1 | 1 Jul Cross Ref random walk with a distribution of waiting Review E, Vol. No. 4 | 28 April Cross Ref on the and for a Diffusion in a Brownian of Probability, Vol. 24, No. 1 | 3 October Cross Ref law and in the of disordered of Statistical Mechanics: Theory and Experiment, Vol. No. | 14 March Cross Ref Fractional equations of Review E, Vol. No. 3 | 29 March Cross Ref Dynamics of a quantum particle in disordered systems with of Statistical Mechanics: Theory and Experiment, Vol. No. | 18 February Cross Ref particle in systems anomalous diffusion: the of weak ergodicity Physics, Vol. 13, No. 5 | 1 Jan Cross Ref diffusion in a and time-dependent energy of Statistical Mechanics: Theory and Experiment, Vol. No. 12 | 6 December Cross Ref The of of Statistical Mechanics: Theory and Experiment, Vol. No. 11 | 15 November Cross Ref random walk of (Europhysics Letters), Vol. No. 3 | 23 November Cross Ref the scaling