6 papers · 1 filter
Kolmogorov invariant torus theorem for weakly interacting particles I: Full dimensional tori
Dmitry Dolgopyat, Bassam Fayad, Jaime Paradela
We develop an abstract KAM theorem for systems of infinitely many interacting particles with decaying masses and all-to-all interactions. Using this framework, we construct full-di…
On Rapid mixing for random walks on nilmanifolds
Dmitry Dolgopyat, Spencer Durham, Minsung Kim
We prove rapid mixing for almost all random walks generated by translations on an arbitrary nilmanifold under mild assumptions on the size of . For several classical classes…
On equivalence of quenched and annealed statistical properties for conservative IID random dynamical systems
Jonathan DeWitt, Dmitry Dolgopyat
In this paper, we prove several theorems relating annealed exponential mixing of the two-point motion with quenched properties of the one-point motion for conservative IID random d…
An analogue of Law of Iterated Logarithm for Heavy Tailed Random Variables
Dmitry Dolgopyat, Sixu Liu
We establish functional limit theorems for ergodic sums of observables with power singularities for expanding circle maps. In the regime where the observables have infinite varianc…
Conservative Coexpanding on Average Diffeomorphisms
Jonathan DeWitt, Dmitry Dolgopyat
We show that the generator of a conservative IID random system whose dynamics expands on average codimension planes has an essential spectral radius strictly smaller than o…
Expanding on average diffeomorphisms of surfaces: exponential mixing
Jonathan DeWitt, Dmitry Dolgopyat
We show that the Bernoulli random dynamical system associated to a expanding on average tuple of volume preserving diffeomorphisms of a closed surface is exponentially mixing.