Unequal Twins: Probability Distributions Do Not Determine Everything

Yasmine Meroz, Igor M. Sokolov, and Joseph Klafter
Phys. Rev. Lett. 107, 260601 – Published 19 December 2011
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Abstract

It is the common lore to assume that knowing the equation for the probability distribution function (PDF) of a stochastic model as a function of time tells the whole picture defining all other characteristics of the model. We show that this is not the case by comparing two exactly solvable models of anomalous diffusion due to geometric constraints: the comb model and the random walk on a random walk. We show that though the two models have exactly the same PDFs, they differ in other respects, like their first passage time distributions, their autocorrelation functions, and their aging properties.

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  • Received 6 August 2011

DOI:https://doi.org/10.1103/PhysRevLett.107.260601

© 2011 American Physical Society

Authors & Affiliations

Yasmine Meroz1,*, Igor M. Sokolov2, and Joseph Klafter1

  • 1School of Chemistry, Raymond & Beverly Sackler Faculty of Exact Sciences, Tel-Aviv University, Tel Aviv 69978, Israel
  • 2Institut für Physik, Humboldt-Universität zu Berlin, Newtonstrasse 15, D-12489 Berlin, Germany

  • *merozyas@post.tau.ac.il

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Issue

Vol. 107, Iss. 26 — 23 December 2011

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