Origins and applications of the Montroll-Weiss continuous time random walk

Regular Article
Part of the following topical collections:
  1. Topical Issue: Continuous Time Random Walk Still Trendy: Fifty-year History, Current State and Outlook


The Continuous Time Random Walk (CTRW) was introduced by Montroll and Weiss in 1965 in a purely mathematical paper. Its antecedents and later applications beginning in 1973 are discussed, especially for the case of fractal time where the mean waiting time between jumps is infinite.


  1. 1.
    A.A. Markov, Bull. Imp. Acad. Sci. St. Petersburg 7, 153 (1913)Google Scholar
  2. 2.
    P. Lévy, Proceedings from the International Congress of Mathematicians 3, 416 (1954)Google Scholar
  3. 3.
    W.L. Smith, Proc. Roy. Soc. Ser. A 232, 6 (1955)ADSCrossRefGoogle Scholar
  4. 4.
    E.W. Montroll, G.H. Weiss, J. Math. Phys. 6, 167 (1965)ADSCrossRefGoogle Scholar
  5. 5.
    H. Scher, M. Lax, Phys. Rev. B 7, 4491 (1973)ADSMathSciNetCrossRefGoogle Scholar
  6. 6.
    H. Scher, E.W. Montroll, Phys. Rev. B 12, 2455 (1975)ADSCrossRefGoogle Scholar
  7. 7.
    V.M. Kenkre, E.W. Montroll, M.F. Shlesinger, J. Stat. Phys. 9, 45 (1973)ADSCrossRefGoogle Scholar
  8. 8.
    M.F. Shlesinger, J. Stat. Phys. 10, 421 (1974)ADSCrossRefGoogle Scholar
  9. 9.
    M.F. Shlesinger, E.W. Montroll, Proc. Natl. Acad. Sci. 81, 1280 (1980)ADSCrossRefGoogle Scholar
  10. 10.
    E.W. Montroll, J. Math. Phys. XXV 1, 37 (1946)MathSciNetCrossRefGoogle Scholar
  11. 11.
    E.W. Montroll, Stochastic Processes in Mathematical Phys. Eng. Sci. Proc. Symp. Appl. Math. XVI, 193 (1964)CrossRefGoogle Scholar
  12. 12.
    R. Courant, K. Friedrichs, H. Lewy, Über die partiellen Differenzengleichungen der Mathematischen Physik, Mathematische Annalen (in German) 100, 32 (1928)ADSCrossRefMATHGoogle Scholar
  13. 13.
    H. Scher, M.F. Shlesinger, J.T. Bendler, Phys. Today 44, 26 (1991)ADSCrossRefGoogle Scholar
  14. 14.
    G.H. Weiss, Aspects and Applications of the Random Walk, Random Materials and Processes (North-Holland Publishing Co., Amsterdam, 1994)Google Scholar
  15. 15.
    J. Masoliver, M. Montero, J. Perelló, G.H. Weiss, J. Econ. Behavior & Organization 61, 577 (2006)CrossRefGoogle Scholar

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© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Office of Naval ResearchArlingtonUSA

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