Relative complexity of random walks in random sceneries

Abstract

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 α-stable CLT ($1<\alpha \le 2$). The results give invariants for relative isomorphism of these.

Published in at http://dx.doi.org/10.1214/11-AOP688 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (2)

• Random walk in random scenery: A survey of some recent results
• Weak invariance principle for the local times of partial sums of Markov Chains

Cited by in corpus (6)

• Scenery entropy as an invariant of RWRS processes
• Entropy dimension for Deterministic Walks in Random Sceneries
• Packing topological entropy for amenable group actions
• Boundary of the Range of a random walk and the Fölner property
• Optimal bounds for self-intersection local times
• Scenery Reconstruction for Random Walk on Random Scenery Systems