A Study of the Restricted Random Walk

Previous article Next article A Study of the Restricted Random WalkR. Sherman Lehman and George H. WeissR. Sherman Lehman and George H. Weisshttps://doi.org/10.1137/0106018PDFPDF PLUSBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] W. Kuhn, Über die Gestalt fadenförmiger Molekule in Losungen, Kolloid Zeit., 68 (1934), 2–14 10.1007/BF01451681 CrossrefGoogle Scholar[2] G. King, Final Report: Research in the Physical and Structural Analysis of High Polymers by Punched Card Methods, Contract N6onr-228 with A. D. Little, Inc., Google Scholar[3] B. Zimm and , W. Stockmayer, The dimensions of chain molecules containing branches and rings, J. Chem. Phys., 17 (1949), 1301–1314 10.1063/1.1747157 CrossrefISIGoogle Scholar[4] W. Kuhn and , H. Kuhn, Rigidity of chain molecules and its determination from viscosity and flow birefringence in dilute solutions, J. Colloid Sci., 3 (1948), 11–32 10.1016/0095-8522(48)90003-8 CrossrefGoogle Scholar[5] F. Bueche, , P. Debye and , W. Cashin, Expressions for turbidities, J. Chem. Phys., 19 (1951), 803– 10.1063/1.1748381 CrossrefISIGoogle Scholar[6] Lord Rayleigh, James Bernoulli's theorem in probability, Phil. Mag., 47 (1899), 246–251 CrossrefGoogle Scholar[7] S. Chandresekhar, Stochastic problems in physics and astronomy, Rev. Modern Phys., 15 (1943), 1–89 10.1103/RevModPhys.15.1 MR0008130 CrossrefGoogle Scholar[8] Georg Pólya, Über eine Aufgabe der Wahrscheinlichkeitsrechnung betreffend die Irrfahrt im Straßennetz, Math. Ann., 84 (1921), 149–160 MR1512028 CrossrefGoogle Scholar[9] Elliott W. Montroll, Markoff chains and excluded volume effect in polymer chains, J. Chem. Phys., 18 (1950), 734–743 10.1063/1.1747735 MR0036468 CrossrefISIGoogle Scholar[10] H. L. Frisch, , F. C. Collins and , B. Friedman, Excluded volume effect in polymer chains. I, J. Chem. Phys., 19 (1951), 1402–1409 10.1063/1.1748068 MR0044421 CrossrefISIGoogle Scholar[11] R. Rubin, The excluded volume effect in polymer chains and the analogous random walk problem, J. Chem. Phys., 20 (1952), 1940– 10.1063/1.1700344 CrossrefISIGoogle Scholar[12] B. H. Zimm, , W. H. Stockmayer and , M. Fixman, Excluded volume in polymer chains, J. Chem. Phys., 21 (1953), 1716–1723 10.1063/1.1698650 MR0057772 CrossrefISIGoogle Scholar[13] H. James, The volume exclusion effect in flexible chains, J. Chem. Phys., 21 (1953), 1628–1636 10.1063/1.1698634 CrossrefISIGoogle Scholar[14] F. Wall, Mean dimensions of rubber-like molecules, J. Chem. Phys., 21 (1953), 1914–1919 10.1063/1.1698717 CrossrefISIGoogle Scholar[15] E. Teramoto, Statistical theory of chain molecules, Proceedings of the International Conference on Theoretical Physics held in Kyoto, 1953, 409–414 Google Scholar[16] J. M. Hammersley and , K. W. Morton, Poor man's Monte Carlo, J. Roy. Statist. Soc. Ser. B., 16 (1954), 23–38; discussion 61–75 MR0064475 0055.36901 Google Scholar[17] M. Rosenbluth and , A. Rosenbluth, Monte Carlo calculation of the average extension of molecular chains, J. Chem. Phys., 23 (1955), 356–359 10.1063/1.1741967 CrossrefISIGoogle Scholar[18] F. Wall, , L. Hiller and , D. Wheeler, Statistical computation of the mean dimensions of macromolecules, J. Chem. Phys., 22 (1954), 1036–1041, 23 (1955), pp. 913–921, 2314–2321. 10.1063/1.1740258 CrossrefISIGoogle Scholar[19] M. L. Juncosa, Random Number Generation on the BRL High-Speed Computing Machines, BRL Report 855, Ballistic Research Labs., Aberdeen Proving Ground, Md., 1948 Google Scholar[20] A. M. Mood, The distribution theory of runs, Ann. Math. Statistics, 11 (1940), 367–392 MR0003493 0024.05301 CrossrefGoogle Scholar[21] E. Voronaskaja, Détermination de la forme asymptotique d'approximation des fonctions par les polynomes de M. Bernstein, C. R. Acad. Sci. URSS, (1932), 79–85 Google Scholar[22] R. S. Lehman and , G. H. Weiss, A study of the Restricted Random Walk, BRL Report 1017, Ballistic Research Labs., Aberdeen Proving Ground, Md., 1957 0090.34902 Google Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Volume 6, Issue 3| 1958Journal of the Society for Industrial and Applied Mathematics199-319 History Submitted:09 December 1957Published online:10 July 2006 InformationCopyright © 1958 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0106018Article page range:pp. 257-278ISSN (print):0368-4245ISSN (online):2168-3484Publisher:Society for Industrial and Applied Mathematics