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We consider the geodesic flow for a rank one non-positive curvature closed manifold. We prove an asymptotic version of the Central Limit Theorem for families of measures constructed from regular closed geodesics converging to the…

Dynamical Systems · Mathematics 2021-08-11 Daniel J. Thompson , Tianyu Wang

We consider deterministic random walks on the real line driven by irrational rotations, or equivalently, skew product extensions of a rotation by $\alpha$ where the skewing cocycle is a piecewise constant mean zero function with a jump by…

Dynamical Systems · Mathematics 2017-05-23 Michael Bromberg , Corinna Ulcigrai

We prove a Functional Central Limit Theorem for the position of a Tagged Particle in the one-dimensional Asymmetric Simple Exclusion Process in the hyperbolic scaling, starting from a Bernoulli product measure conditioned to have a particle…

Probability · Mathematics 2007-05-23 Patricia Goncalves

We obtain large deviations estimates for both sequential and random compositions of intermittent maps. We also address the question of whether or not centering is necessary for the quenched central limit theorems (CLT) obtained by Nicol,…

Dynamical Systems · Mathematics 2020-08-14 Matthew Nicol , Felipe Perez Pereira , Andrew Torok

The Central Limit Theorem (CLT) is one of the most fundamental results in statistics. It states that the standardized sample mean of a sequence of $n$ mutually independent and identically distributed random variables with finite first and…

In this work, we examine the finite temperature properties of the CPT-even and Lorentz-invariance-violating (LIV) electrodynamics of the standard model extension, represented by the term $W_{\alpha \nu \rho \phi}F^{\alpha \nu}F^{\rho…

High Energy Physics - Theory · Physics 2009-11-05 Rodolfo Casana , Manoel M. Ferreira , Josberg S. Rodrigues , Madson R. O. Silva

When the underlying random variables are Gaussian, the classical Central Limit Theorem (CLT) is trivial, but the functional CLT is not. The objective of the paper is to investigate the functional CLT for stationary Gaussian processes in the…

Probability · Mathematics 2022-09-20 S. V. Lototsky

We investigate the decay rates of correlations for nonuniformly hyperbolic systems with or without singularities, on piecewise H\"older observables. By constructing a new scheme of coupling methods using the probability renewal theory, we…

Dynamical Systems · Mathematics 2019-06-28 Sandro Vaienti , Hong-Kun Zhang

Stochastic dynamical systems consisting of non-invertible continuous maps on an interval are studied. It is proved that if they satisfy the recently introduced so-called $\mu$-injectivity and some mild assumptions, then proximality,…

Dynamical Systems · Mathematics 2025-12-11 Sander C. Hille , Katarzyna Horbacz , Hanna Oppelmayer , Tomasz Szarek

We consider Betti numbers of the excursion of a smooth Euclidean Gaussian field restricted to a rectangular window, in the asymptotics where the window grows to R^d . With motivations coming from Topological Data Analysis, we derive a…

Probability · Mathematics 2025-12-16 Christian Hirsch , Raphaël Lachièze-Rey

We continue the study of non-invertible topological dynamical systems with expanding behavior. We introduce the class of {\em finite type} systems which are characterized by the condition that, up to rescaling and uniformly bounded…

Dynamical Systems · Mathematics 2016-06-22 Peter Haïssinsky , Kevin M. Pilgrim

In this paper we will prove a functional central limit theorems for "nonconventional" sums indexed by polynomial arrays.

Probability · Mathematics 2019-12-18 Yeor Hafouta

This work investigates a dynamical system functioning as a nonsmooth adaptation of the continuous Newton method, aimed at minimizing the sum of a primal lower-regular and a locally Lipschitz function, both potentially nonsmooth. The…

Optimization and Control · Mathematics 2024-12-10 Juan Guillermo Garrido , Pedro Pérez-Aros , Emilio Vilches

We prove a sequence of limiting results about weakly dependent stationary and regularly varying stochastic processes in discrete time. After deducing the limiting distribution for individual clusters of extremes, we present a new type of…

Probability · Mathematics 2017-12-05 Bojan Basrak , Hrvoje Planinic , Philippe Soulier

A recent paper by Lien et al. (2025) introduces the "colored linear inverse model" (colored LIM), in which stochastic forcing is modeled using Ornstein-Uhlenbeck colored noise rather than idealized white noise. In that work, it is shown…

Atmospheric and Oceanic Physics · Physics 2026-04-06 Cristian Martinez-Villalobos

We consider a random field, defined on an integer-valued d-dimensional lattice, with covariance function satisfying a condition more general than summability. Such condition appeared in the well-known Newman's conjecture concerning the…

Probability · Mathematics 2011-04-22 Alexander Bulinski

We consider a multidimensional random walk in a product random environment with bounded steps, transience in some spatial direction, and high enough moments on the regeneration time. We prove an invariance principle, or functional central…

Probability · Mathematics 2015-05-13 Firas Rassoul-Agha , Timo Seppalainen

We prove a central limit theorem for the linear statistics of one-dimensional log-gases, or $\beta$-ensembles. We use a method based on a change of variables which allows to treat fairly general situations, including multi-cut and, for the…

Mathematical Physics · Physics 2018-02-08 Florent Bekerman , Thomas Leblé , Sylvia Serfaty

Using the framework of Colombeau algebras of generalized functions, we prove the existence and uniqueness results for global generalized solvability of semilinear hyperbolic systems with nonlinear nonlocal boundary conditions. We admit…

Analysis of PDEs · Mathematics 2025-12-10 Irina Kmit

We extend to the case of moving solitons, the result on asymptotic stability of ground states of the NLS with a short range linear potential obtained by the author in a previous paper. Now we drop the potential and allow moving solitons.…

Analysis of PDEs · Mathematics 2012-02-23 Scipio Cuccagna