Unequal twins: Probability distributions do not determine everything

Yasmine Meroz*, Igor M. Sokolov, Joseph Klafter

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Article number260601
JournalPhysical Review Letters
Issue number26
StatePublished - 19 Dec 2011


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