166 citations · 241 across the 14 of their papers we have counts for
15 papers
Exponential growth of random infinite Fibonacci sequences
Ilya Goldsheid, Ofer Zeitouni
We consider the recursion , where are i.i.d. (Bernoulli) random variables taking values in , and , for $j…
Sets of non-Lyapunov behaviour for scalar and matrix Schrödinger cocycles
Ilya Goldsheid, Sasha Sodin
We discuss the growth of the singular values of symplectic transfer matrices associated with ergodic discrete Schrödinger operators in one dimension, with scalar and matrix-valued…
Lower bounds on Anderson-localised eigenfunctions on a strip
Ilya Goldsheid, Sasha Sodin
It is known that the eigenfunctions of a random Schrödinger operator on a strip decay exponentially, and that the rate of decay is not slower than prescribed by the slowest Lyapuno…
Constructive approach to limit theorems for recurrent diffusive random walks on a strip
Dmitry Dolgopyat, Ilya Goldsheid
We consider recurrent diffusive random walks on a strip. We present constructive conditions on Green functions of finite sub-domains which imply a Central Limit Theorem with polyno…
Exponential growth of products of non-stationary Markov-dependent matrices
Ilya Goldsheid
Let , be a non-stationary Markov chain with phase space and let be a sequence of functions on with valu…
Local Limit Theorems for Random Walks in a Random Environment on a Strip
Dmitry Dolgopyat, Ilya Goldsheid
The paper consists of two parts. In the first part we review recent work on limit theorems for random walks in random environment (RWRE) on a strip with jumps to the nearest layers…