Isomorphism of random walks

Jon Aaronson*, Michael Keane

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We show that any two aperiodic, recurrent random walks on the integers whose jump distributions have finite seventh moment, are isomorphic as infinite measure preserving transformations. The method of proof involved uses a notion of equivalence of renewal sequences, and the "relative" isomorphism of Bernoulli shifts respecting a common state lumping with the same conditional entropy. We also prove an analogous result for random walks on the two dimensional integer lattice.

Original languageEnglish
Pages (from-to)37-63
Number of pages27
JournalIsrael Journal of Mathematics
Issue number1-3
StatePublished - Feb 1994


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