Relative complexity of random walks in random sceneries

Jon Aaronson*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


Relative complexity measures the complexity of a probability preserving transformation relative to a factor being a sequence of random variables whose exponential growth rate is the relative entropy of the extension. We prove distributional limit theorems for the relative complexity of certain zero entropy extensions: RWRSs whose associated random walks satisfy the a- stable CLT (1< α ≤ 2). The results give invariants for relative isomorphism of these.

Original languageEnglish
Pages (from-to)2460-2482
Number of pages23
JournalAnnals of Probability
Issue number6
StatePublished - 2012


  • Entropy dimension
  • Local time
  • Random walk in random scenery
  • Relative complexity
  • Symmetric stable process
  • [T, T] transformation


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