Accurate estimation of the survival probability for trapping in two dimensions

In this work we study the mean survival probability Phi(n,c) of random walks on a two-dimensional lattice in the presence of traps of concentration c, as a function of the number of steps n. The computation of this quantity is performed indirectly by using the distribution of the number of sites visited S(n). In order to achieve an accurate description of this distribution we use a combination of numerical techniques. The method allows an accurate calculation of Phi down to very small values (of the order of 10(-100), for example), which is not possible via direct simulations. The survival probability is analyzed in terms of an asymptotic expansion, following the results of Donsker and Varadhan [Commun. Pure Appl. Math. 28, 525 (1975); 32, 721 (1979)], and by using the outcome of a scaling ansatz, as described in our earlier work.