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Recurrent random walks in random and quasi-periodic environments on a strip

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Periodic and Ergodic Spectral Problems

This is joint work with D. Dolgopyat

We prove that a recurrent random walk (RW) in random environment (RE) on a strip which does not obey the Sinai law exhibits the Central Limit asymptotic behaviour.

We also show that there exists a collection of proper sub-varieties in the space of transition probabilities such that

1. If RE is stationary and ergodic and the transition probabilities are concentrated on one of sub-varieties from our collection then the CLT holds; 2. If the environment is i.i.d then the above condition is also necessary for the CLT .

As an application of our techniques we prove the CLT for quasi-periodic environments with Diophantine frequencies. One-dimensional RWRE with bounded jumps are a particular case of the strip model.

This talk is part of the Isaac Newton Institute Seminar Series series.

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