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

Date: 
Wednesday 8th April 2015 - 11:30 to 12:30
Venue: 
INI Seminar Room 1
Abstract: 
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.

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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons