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Related papers: Dynamical large deviations of reflected diffusions

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We investigate the extreme value statistics of a one-dimensional Brownian motion (with the diffusion constant $D$) during a time interval $\left[0, t \right]$ in the presence of a reflective boundary at the origin, starting from a positive…

Statistical Mechanics · Physics 2024-01-26 Feng Huang , Hanshuang Chen

The so-called 'Level 2.5' general result for the large deviations of the joint probability of the density and of the currents for Markov Jump processes is applied to the case of $N$ independent particles on a ring with random transition…

Disordered Systems and Neural Networks · Physics 2021-05-12 Cecile Monthus

The aim of this paper is to discuss the appropriate modelling of in- and outflow boundary conditions for nonlinear drift-diffusion models for the transport of particles including size exclusion and their effect on the behaviour of…

Analysis of PDEs · Mathematics 2016-11-03 Martin Burger , Jan-Frederik Pietschmann

Employing large deviation theory, we explore current fluctuations of underdamped Brownian motion for the paradigmatic example of a single particle in a one dimensional periodic potential. Two different approaches to the large deviation…

Statistical Mechanics · Physics 2018-03-12 Lukas P. Fischer , Patrick Pietzonka , Udo Seifert

We study exclusion processes on the integer lattice in which particles change their velocities due to stickiness. Specifically, whenever two or more particles occupy adjacent sites, they stick together for an extended period of time, and…

Probability · Mathematics 2016-08-11 Miklós Z. Rácz , Mykhaylo Shkolnikov

The paper is devoted to constructing the global solutions around global Maxwellians to the initial-boundary value problem on the Boltzmann equation in general bounded domains with isothermal diffuse reflection boundaries. We allow a class…

Analysis of PDEs · Mathematics 2018-11-14 Renjun Duan , Yong Wang

We prove the large deviation principle for the trajectory of a broad class of mean field interacting Markov jump processes via a general analytic approach based on viscosity solutions. Examples include generalized Ehrenfest models as well…

Probability · Mathematics 2016-06-24 Richard Kraaij

The Large Deviation Principle is established for stochastic models defined by past-dependent non linear recursions with small noise. In the Markov case we use the result to obtain an explicit expression for the asymptotics of exit time.

Probability · Mathematics 2007-05-23 F. Klebaner , R. Liptser

We consider the superposition of a symmetric simple exclusion dynamics, speeded-up in time, with a spin-flip dynamics in a one-dimensional interval with periodic boundary conditions. We prove the large deviations principle for the empirical…

Probability · Mathematics 2018-05-01 Jonathan Farfan , Claudio Landim , Kenkichi Tsunoda

This paper is mainly concerned with the large deviation principle of the fractional McKean-Vlasov stochastic reaction-diffusion equation defined on R^n with polynomial drift of any degree. We first prove the well-posedness of the underlying…

Probability · Mathematics 2024-06-18 Zhang Chen , Bixiang Wang

The large deviations properties of trajectory observables for chaotic non-invertible deterministic maps as studied recently by N. R. Smith, Phys. Rev. E 106, L042202 (2022) and by R. Gutierrez, A. Canella-Ortiz, C. Perez-Espigares,…

Statistical Mechanics · Physics 2024-01-30 Cecile Monthus

Considering the example of interacting Brownian particles we present a linear response derivation of the boundary condition for the corresponding hydrodynamic description (the diffusion equation). This requires us to identify a non-analytic…

Statistical Mechanics · Physics 2009-11-07 M. Fuchs , K. Kroy

We study Lorentz processes in two different settings. Both cases are characterized by infinite expectation of the free-flight times, contrary to what happens in the classical Gallavotti-Spohn models. Under a suitable Boltzmann-Grad type…

Probability · Mathematics 2025-09-23 Lorenzo Facciaroni , Costantino Ricciuti , Enrico Scalas , Bruno Toaldo

Several integrate-to-threshold models with differing temporal integration mechanisms have been proposed to describe the accumulation of sensory evidence to a prescribed level prior to motor response in perceptual decision-making tasks. An…

Neurons and Cognition · Quantitative Biology 2009-01-16 Xiang Zhou , KongFatt Wong-Lin , Philip Holmes

We propose a method for approximating the large deviation rate function of time-integrated observables of diffusion processes, used in statistical physics to characterize the fluctuations of nonequilibrium systems. The method is based on…

Statistical Mechanics · Physics 2026-01-15 Pelerine Tsobgni Nyawo , Hugo Touchette

We establish the fractional diffusion limit of the kinetic scattering equation with diffusive boundary condition in a strongly convex bounded domain $\mathcal{D}\subset\mathbb{R}^d$. According to the nature of the boundary condition, two…

Probability · Mathematics 2025-12-22 Loïc Béthencourt , Nicolas Fournier

We study using large deviation theory the fluctuations of time-integrated functionals or observables of the unbiased random walk evolving on Erd\"os-R\'enyi random graphs, and construct a modified, biased random walk that explains how these…

Statistical Mechanics · Physics 2019-03-06 Francesco Coghi , Jules Morand , Hugo Touchette

Constrained Markov processes, such as reflecting diffusions, behave as an unconstrained process in the interior of a domain but upon reaching the boundary are controlled in some way so that they do not leave the closure of the domain. In…

Probability · Mathematics 2019-12-06 Cristina Costantini , Thomas G. Kurtz

We develop an encounter-based approach for describing restricted diffusion with a gradient drift towards a partially reactive boundary. For this purpose, we introduce an extension of the Dirichlet-to-Neumann operator and use its eigenbasis…

Chemical Physics · Physics 2022-10-10 Denis S. Grebenkov

We prove a large-deviation principle (LDP) for the sample paths of jump Markov processes in the small noise limit when, possibly, all the jump rates vanish uniformly, but slowly enough, in a region of the state space. We further discuss the…

Probability · Mathematics 2021-02-26 Andrea Agazzi , Luisa Andreis , Robert I. A. Patterson , D. R. Michiel Renger