Title: Entropy and random walks on random sceneries

Abstract: Let X = X_{0}, X_{1}, … be a stationary sequence of random variables defining a sequence space Σ with shift map σ and let (T_{t}, Ω) be an ergodic flow. Then the endomorphism T̂_{X}(x, ω) = (σ(x), T_{x_{0}}(ω)) is known as a random walk on a random scenery. I am interested in when two such transformations can be measure-theoretically isomorphic. Heicklen, Hoffman and Rudolph have proven that within the class of T, T^{−1} endomorphisms (where X = {±1}^{ℕ} with uniform measure and (T, Ω) is an invertible transformation with T^{2} ergodic), the entropy of T is an isomorphism invariant. In this talk, I will discuss a generalization of this result to a broader class of random walks on random sceneries.