The theory of one-dimensional ergodic operators involves a beautiful synthesis of ideas from
dynamical systems, topology, and analysis. Additionally, this setting includes many models …

Generalization analyses of deep learning typically assume that the training converges to a
fixed point. But, recent results indicate that in practice, the weights of deep neural networks …

We put forward a new method for obtaining quantitative lower bounds on the top Lyapunov
exponent of stochastic differential equations. Our method combines (i) a new identity …

This paper develops nonasymptotic growth and concentration bounds for a product of
independent random matrices. These results sharpen and generalize recent work of …

Products of M iid random matrices of size N× N are related to classical limit theorems in
probability theory (N= 1 and large M), to Lyapunov exponents in dynamical systems (finite N …

We consider random products of SL (2, R) matrices that depend on a parameter in a non-
uniformly hyperbolic regime. We show that if the dependence on the parameter is monotone …

We prove a non-stationary analog of the Furstenberg Theorem on random matrix products
(that can be considered as a matrix version of the law of large numbers). Namely, under a …

We prove that all Galerkin truncations of the 2d stochastic Navier–Stokes equations in
vorticity form on any rectangular torus subjected to hypoelliptic, additive stochastic forcing …

We consider the top Lyapunov exponent associated to a dissipative linear evolution
equation posed on a separable Hilbert or Banach space. In many applications in partial …

Products of $ M $ iid random matrices of size $ N\times N $ are related to classical limit
theorems in probability theory ($ N= 1$ and large $ M $), to Lyapunov exponents in …