22 citations · 116 across the 14 of their papers we have counts for
18 papers
Rigorous and effective numerics for Liverani-Saussol-Vaienti maps
Alexey Korepanov, YuTong Wei, Caroline Wormell
We make highly accurate numerical estimates of basic properties of the invariant measure for Liverani-Saussol-Vaienti intermittent maps, an archetypal slowly mixing dynamical syste…
Rates of memory loss for null recurrent Markov chains
Ilya Chevyrev, Alexey Korepanov
Orey (1962) proved that for an irreducible, aperiodic, and recurrent Markov chain with transition operator , the sequence converges to zero in total variation for a…
Superdiffusive limits beyond the Marcus regime for deterministic fast-slow systems
Ilya Chevyrev, Alexey Korepanov, Ian Melbourne
We consider deterministic fast-slow dynamical systems of the form \[ x_{k+1}^{(n)} = x_k^{(n)} + n^{-1} A(x_k^{(n)}) + n^{-1/α} B(x_k^{(n)}) v(y_k), \quad y_{k+1} = Ty_k, \] where…
Rates in almost sure invariance principle for nonuniformly hyperbolic maps
C Cuny, J Dedecker, A Korepanov +1
We prove the Almost Sure Invariance Principle (ASIP) with close to optimal error rates for nonuniformly hyperbolic maps. We do not assume exponential contraction along stable leave…
Rates of mixing for the measure of maximal entropy of dispersing billiard maps
Mark F. Demers, Alexey Korepanov
In a recent work, Baladi and Demers constructed a measure of maximal entropy for finite horizon dispersing billiard maps and proved that it is unique, mixing and moreover Bernoulli…
Deterministic homogenization under optimal moment assumptions for fast-slow systems. Part 1
Alexey Korepanov, Zemer Kosloff, Ian Melbourne
We consider deterministic homogenization (convergence to a stochastic differential equation) for multiscale systems of the form \[ x_{k+1} = x_k + n^{-1} a_n(x_k,y_k) + n^{-1/2} b_…
Superdiffusive limits for deterministic fast-slow dynamical systems
Ilya Chevyrev, Peter K. Friz, Alexey Korepanov +1
We consider deterministic fast-slow dynamical systems on of the form \[ \begin{cases} x_{k+1}^{(n)} = x_k^{(n)} + n^{-1} a(x_k^{(n)}) + n^{-1/α} b(x_k^{(n)})…
Deterministic homogenization under optimal moment assumptions for fast-slow systems. Part 2
Ilya Chevyrev, Peter K. Friz, Alexey Korepanov +2
We consider deterministic homogenization for discrete-time fast-slow systems of the form …
Rates in almost sure invariance principle for quickly mixing dynamical systems
C Cuny, J Dedecker, A Korepanov +1
For a large class of quickly mixing dynamical systems, we prove that the error in the almost sure approximation with a Brownian motion is of order O((log n)^a) with a 2. Spec…
On the timescale at which statistical stability breaks down
Neil Dobbs, Alexey Korepanov
In dynamical systems, understanding statistical properties shared by most orbits and how these properties depend on the system are basic and important questions. Statistical proper…
Rates in almost sure invariance principle for slowly mixing dynamical systems
C. Cuny, J. Dedecker, A. Korepanov +1
We prove the one-dimensional almost sure invariance principle with essentially optimal rates for slowly (polynomially) mixing deterministic dynamical systems, such as Pomeau-Mannev…
Multiscale systems, homogenization, and rough paths
Ilya Chevyrev, Peter K. Friz, Alexey Korepanov +2
In recent years, substantial progress was made towards understanding convergence of fast-slow deterministic systems to stochastic differential equations. In contrast to more classi…
Rates in almost sure invariance principle for dynamical systems with some hyperbolicity
Alexey Korepanov
We prove the almost sure invariance principle with rate for every for Hölder continuous observables on nonuniformly expanding and nonuniforml…
Equidistribution for nonuniformly expanding dynamical systems, and application to the almost sure invariance principle
Alexey Korepanov
Let be a nonuniformly expanding dynamical system, such as logistic or intermittent map. Let be an observable and $v_n = \sum_{k=0}^…
Martingale-coboundary decomposition for families of dynamical systems
A. Korepanov, Z. Kosloff, I. Melbourne
We prove statistical limit laws for sequences of Birkhoff sums of the type where is a family of nonuniformly hyperbolic transformations. The…
Explicit coupling argument for nonuniformly hyperbolic transformations
A. Korepanov, Z. Kosloff, I. Melbourne
The transfer operator corresponding to a uniformly expanding map enjoys good spectral properties. Here it is verified that coupling yields explicit estimates that depend continuous…
Averaging and rates of averaging for uniform families of deterministic fast-slow skew product systems
A. Korepanov, Z. Kosloff, I. Melbourne
We consider families of fast-slow skew product maps of the form \begin{align*} x_{n+1} = x_n+εa(x_n,y_n,ε), \quad y_{n+1} = T_εy_n, \end{align*} where is a family of nonunifo…
Linear response for intermittent maps with summable and nonsummable decay of correlations
Alexey Korepanov
We consider a family of Pomeau-Manneville type interval maps , parametrized by , with the unique absolutely continuous invariant probability measures , and ra…