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We study rates of mixing for small random perturbations of one dimensional Lorenz maps. Using a random tower construction, we prove that, for Holder observables, the random system admits exponential rates of quenched correlation decay.

Dynamical Systems · Mathematics 2021-11-29 Andrew Larkin

This study deals with continuous limits of interacting one-dimensional diffusive systems, arising from stochastic distortions of discrete curves with various kinds of coding representations. These systems are essentially of a…

Statistical Mechanics · Physics 2011-09-09 Guy Fayolle , Cyril Furtlehner

We obtain large and moderate deviation estimates, as well as concentration inequalities, for a class of nonuniformly expanding maps with stretched exponential decay of correlations. In the large deviation regime, we also exhibit examples…

Probability · Mathematics 2022-01-26 C Cuny , J Dedecker , F Merlevède

Consider a proper metric space X and a sequence of i.i.d. random continuous mappings F_n from X to X. It induces the stochastic dynamical system (SDS) X_n^x = F_n(X_{n-1}^x) starting at x in X. In this paper, we study existence and…

Probability · Mathematics 2012-12-05 Marc Peigné , Wolfgang Woess

The turnaround epoch of gravitational collapse is examined by means of relativistic Lagrangian perturbation theory. Averaged, scalar equations applied to the fluid's evolution reveal some scale-independent universality of parameters for a…

General Relativity and Quantum Cosmology · Physics 2020-01-01 Jan J. Ostrowski

We establish Lipschitz stability properties for a class of inverse problems. In that class, the associated direct problem is formulated by an integral operator Am depending non-linearly on a parameter m and operating on a function u. In the…

Numerical Analysis · Mathematics 2023-02-27 Darko Volkov

We construct a Lipschitz truncation which approximates functions of bounded variation in the area-strict metric. The Lipschitz truncation changes the original function only on a small set similar to Lusin's theorem. Previous results could…

Analysis of PDEs · Mathematics 2019-08-29 Dominic Breit , Lars Diening , Franz Gmeineder

We prove that multimodal maps with an absolutely continuous invariant measure have exponential return time statistics around a.e. point. We also show a `polynomial Gibbs property' for these systems, and that the convergence to the entropy…

Dynamical Systems · Mathematics 2009-04-20 Henk Bruin , Mike Todd

We study the Integrated Density of States of one-dimensional random operators acting on $\ell^2(\mathbb Z)$ of the form $T + V_\omega$ where $T$ is a Laurent (also called bi-infinite Toeplitz) matrix and $V_\omega$ is an Anderson potential…

Mathematical Physics · Physics 2022-10-26 Martin Gebert , Constanza Rojas-Molina

In this paper we are interested in the inverse problem of recovering a compact supported function from its truncated Fourier transform. We derive new Lipschitz stability estimates for the inversion in terms of the truncation parameter. The…

Numerical Analysis · Mathematics 2024-07-10 Mirza Karamehmedović , Martin Sæbye Carøe , Faouzi Triki

We prove decay estimates in the interior for solutions to elliptic equations in divergence form with Lipschitz continuous coefficients. The estimates explicitly depend on the distance from the boundary and on suitable notions of frequency…

Analysis of PDEs · Mathematics 2019-07-12 Michele Di Cristo , Luca Rondi

We study a class of bifurcations generically occurring in dynamical systems with non-mutual couplings ranging from models of coupled neurons to predator-prey systems and non-linear oscillators. In these bifurcations, extended attractors…

Chaotic Dynamics · Physics 2023-08-11 Cheyne Weis , Michel Fruchart , Ryo Hanai , Kyle Kawagoe , Peter B. Littlewood , Vincenzo Vitelli

For a map of the unit interval with an indifferent fixed point, we prove an upper bound for the variance of all observables of $n$ variables $K:[0,1]^n\to\R$ which are componentwise Lipschitz. The proof is based on coupling and decay of…

Dynamical Systems · Mathematics 2009-08-27 J. -R. Chazottes , P. Collet , F. Redig , E. Verbitskiy

We show that quantum effects modify the decay rate of Poincar\'e recurrences P(t) in classical chaotic systems with hierarchical structure of phase space. The exponent p of the algebraic decay P(t) ~ 1/t^p is shown to have the universal…

Condensed Matter · Physics 2009-10-31 Giulio Casati , Giulio Maspero , Dima L. Shepelyansky

We study the asymptotic dynamics of stochastic Young differential delay equations under the regular assumptions on Lipschitz continuity of the coefficient functions. Our main results show that, if there is a linear part in the drift term…

Dynamical Systems · Mathematics 2020-07-31 Nguyen Dinh Cong , Luu Hoang Duc , Phan Thanh Hong

We explore the question whether Lipschitz functions of random variables under various forms of negative correlation satisfy concentration bounds similar to McDiarmid's inequality for independent random variables. We prove such a…

Probability · Mathematics 2018-04-27 Kevin Garbe , Jan Vondrak

We consider the long-term dynamics of the vanishing stepsize subgradient method in the case when the objective function is neither smooth nor convex. We assume that this function is locally Lipschitz and path differentiable, i.e., admits a…

Optimization and Control · Mathematics 2020-06-02 Jerome Bolte , Edouard Pauwels , Rodolfo Rios-Zertuche

Nearly linear recurrences are a generalisation of linear recurrences and are instances of linear time-invariant systems in control theory and linear constraint loops in program analysis. In this paper we formulate the Positivity Problem for…

Dynamical Systems · Mathematics 2026-03-04 Amaury Pouly , Mahsa Shirmohammadi , James Worrell

We develop sufficient analytic conditions for recurrence and transience of non-sectorial perturbations of possibly non-symmetric Dirichlet forms on a general state space. These form an important subclass of generalized Dirichlet forms which…

Probability · Mathematics 2017-10-10 Minjung Gim , Gerald Trutnau

We show that the points that converge to infinity under iteration of the exponential map form a connected subset of the complex plane.

Dynamical Systems · Mathematics 2010-04-08 Lasse Rempe