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We study large deviation properties of systems of weakly interacting particles modeled by It\^{o} stochastic differential equations (SDEs). It is known under certain conditions that the corresponding sequence of empirical measures…

Probability · Mathematics 2012-09-26 Amarjit Budhiraja , Paul Dupuis , Markus Fischer

A hierarchical system of equations is introduced to describe dynamics of `sizes' of infinite clusters which coagulate and fragmentate with homogeneous rates of certain form. We prove that this system of equations is solved weakly by…

Probability · Mathematics 2018-09-03 Kenji Handa

The work concerns deviation estimates for multivalued McKean-Vlasov stochastic differential equations. First of all, we prove the large deviation principle for them by the weak convergence approach. Then the central limit theorem for them…

Probability · Mathematics 2022-08-10 Kun Fang , Huijie Qiao

Homogenization of a spectral problem in a bounded domain with a high contrast in both stiffness and density is considered. For a special critical scaling, two-scale asymptotic expansions for eigenvalues and eigenfunctions are constructed.…

Spectral Theory · Mathematics 2007-11-16 Natalia O. Babych , Ilia V. Kamotski , Valery P. Smyshlyaev

Experimental data are presented on particle correlations and fluctuations in various high-energy multiparticle collisions, with special emphasis on evidence for scaling-law evolution in small phase-space domains. The notions of…

High Energy Physics - Phenomenology · Physics 2009-10-28 E. A. De Wolf , I. M. Dremin , W. Kittel

Extremes of information combining inequalities play an important role in the analysis of sparse-graph codes under message-passing decoding. We introduce new tools for the derivation of such inequalities, and show by means of a concrete…

Information Theory · Computer Science 2012-02-01 Lucas Boczkowski

We prove density and current fluctuations for two examples of symmetric, interacting particle systems with anomalous diffusive behavior: the zero-range process with long jumps and the zero-range process with degenerated bond disorder. As an…

Probability · Mathematics 2009-01-05 M. Jara

We study the rate of decay of correlations for equilibrium states associated to a robust class of non-uniformly expanding maps where no Markov assumption is required. We show that the Ruelle-Perron-Frobenius operator acting on the space of…

Dynamical Systems · Mathematics 2015-06-05 Armando Castro , Paulo Varandas

We establish bounds for the measure of deviation sets associated to continuous observables with respect to not necessarily invariant weak Gibbs measures. Under some mild assumptions, we obtain upper and lower bounds for the measure of…

Dynamical Systems · Mathematics 2011-10-27 Paulo Varandas

When there is no independence, abnormal observations may have a tendency to appear in clusters instead of scattered along the time frame. Identifying clusters and estimating their size are important problems arising in statistics of…

Probability · Mathematics 2020-01-08 Miguel Abadi , Ana Cristina Moreira Freitas , Jorge Milhazes Freitas

We prove sharp estimates for the decay in time of solutions to a rather general class of non-local in time subdiffusion equations on a bounded domain subject to a homogeneous Dirichlet boundary condition. Important special cases are the…

Analysis of PDEs · Mathematics 2013-10-02 Vicente Vergara , Rico Zacher

We prove a Large Deviations Principle (LDP) for systems of diffusions (particles) interacting through their ranks, when the number of particles tends to infinity. We show that the limiting particle density is given by the unique solution of…

Probability · Mathematics 2017-04-05 Amir Dembo , Mykhaylo Shkolnikov , S. R. Srinivasa Varadhan , Ofer Zeitouni

We develop a system-theoretic framework for the structured analysis of distributed optimization algorithms with decomposable cost functions. We model such algorithms as a network of interacting dynamical systems and derive tests for…

Optimization and Control · Mathematics 2026-04-14 Aron Karakai , Jaap Eising , Andrea Martinelli , Florian Dörfler

Contraction analysis establishes exponential incremental convergence of a nonlinear system by solving a linear matrix inequality for a contraction metric, and has become a standard resource for solving problems in nonlinear control and…

Dynamical Systems · Mathematics 2026-03-03 Winfried Lohmiller , Jean-Jacques Slotine

The paper is devoted to establishing some general exponential inequalities for supermartingales. The inequalities improve or generalize many exponential inequalities of Bennett, Freedman, de la Pe\~{n}a, Pinelis and van de Geer. Moreover,…

Probability · Mathematics 2015-01-22 Xiequan Fan , Ion Grama , Quansheng Liu

The article considers systems of interacting particles on networks with adaptively coupled dynamics. Such processes appear frequently in natural processes and applications. Relying on the notion of graph convergence, we prove that for large…

Dynamical Systems · Mathematics 2026-05-20 Sebastian Throm

This study uses the link between extreme value laws and dynamical systems theory to show that important dynamical quantities as the correlation dimension, the entropy and the Lyapunov exponents can be obtained by fitting observables…

Chaotic Dynamics · Physics 2018-05-23 Davide Faranda , Sandro Vaienti

Overdamped stochastic systems maintained far from equilibrium can display sustained oscillations with fluctuations that decrease with the system size. The correlation time of such noisy limit cycles expressed in units of the cycle period is…

Statistical Mechanics · Physics 2025-01-31 Davide Santolin , Gianmaria Falasco

This article is concerned with the fluctuations and the concentration properties of a general class of discrete generation and mean field particle interpretations of nonlinear measure valued processes. We combine an original stochastic…

Probability · Mathematics 2012-11-09 Pierre Del Moral , Emmanuel Rio

This paper investigates the initial-boundary value problem for weakly coupled systems of time-fractional subdiffusion equations with spatially and temporally varying coupling coefficients. By combining the energy method with the coercivity…

Analysis of PDEs · Mathematics 2025-10-16 Zhiyuan Li , Yikan Liu , Kazuma Wada