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We study a diffuse interface model for the flow of two viscous incompressible Newtonian fluids in a bounded domain. The fluids are assumed to be macroscopically immiscible, but a partial mixing in a small interfacial region is assumed in…

Analysis of PDEs · Mathematics 2011-04-01 Helmut Abels

A pathwise large deviation principle in the Wasserstein topology and a pathwise central limit theorem are proved for the empirical measure of a mean-field system of interacting diffusions. The coefficients are path-dependent. The framework…

Probability · Mathematics 2024-10-10 Louis-Pierre Chaintron

In recent work [1] we uncovered intriguing connections between Otto's characterisation of diffusion as entropic gradient flow [16] on one hand and large-deviation principles describing the microscopic picture (Brownian motion) on the other.…

Analysis of PDEs · Mathematics 2014-03-05 Stefan Adams , Nicolas Dirr , Mark A. Peletier , Johannes Zimmer

We consider the interacting Bessel processes, a family of multiple-particle systems in one dimension where particles evolve as individual Bessel processes and repel each other via a log-potential. We consider two limiting regimes for this…

Mathematical Physics · Physics 2015-06-17 Sergio Andraus , Makoto Katori , Seiji Miyashita

The aim of the present paper is to extend the large deviation with discontinuous statistics studied in \cite{BDE} to the diffusion $d\mathbf{x}^\varepsilon = -\{\mathbf{A}^\top (\mathbf{A} \mathbf{x}^\varepsilon - \mathbf{y}) + \mu…

Probability · Mathematics 2016-10-04 Azzouz Dermoune , Khalifa Es-Sebaiy , Youssef Ouknine

This paper studies large deviations of a ``fully coupled" finite state mean-field interacting particle system in a fast varying environment. The empirical measure of the particles evolves in the slow time scale and the random environment…

Probability · Mathematics 2021-06-24 Sarath Yasodharan , Rajesh Sundaresan

In this paper, we propose an efficient Monte Carlo implementation of non-linear FBSDEs as a system of interacting particles inspired by the ideas of branching diffusion method. It will be particularly useful to investigate large and complex…

Computational Finance · Quantitative Finance 2012-04-24 Masaaki Fujii , Akihiko Takahashi

We study large deviations asymptotics for a class of unbounded additive functionals, interpreted as normalized accumulated areas, of one-dimensional Langevin diffusions with sub-linear gradient drifts. Our results provide parametric…

Probability · Mathematics 2023-10-23 Mihail Bazhba , Jose Blanchet , Roger J. A. Laeven , Bert Zwart

We consider the weakly asymmetric exclusion process on a bounded interval with particle reservoirs at the endpoints. The hydrodynamic limit for the empirical density, obtained in the diffusive scaling, is given by the viscous Burgers…

Probability · Mathematics 2009-12-14 Lorenzo Bertini , Claudio Landim , Mustapha Mourragui

We propose an interacting particle system to model the evolution of a system of banks with mutual exposures. In this model, a bank defaults when its normalized asset value hits a lower threshold, and its default causes instantaneous losses…

Probability · Mathematics 2017-05-03 Sergey Nadtochiy , Mykhaylo Shkolnikov

In this paper, we study the large deviation principle of invariant measures of stochastic reaction-diffusion lattice systems driven by multiplicative noise. We first show that any limit of a sequence of invariant measures of the stochastic…

Probability · Mathematics 2024-05-07 Bixiang Wang

We formulate large deviations principle (LDP) for diffusion pair $(X^\epsilon,\xi^\epsilon)=(X_t^\epsilon,\xi_t^\epsilon)$, where first component has a small diffusion parameter while the second is ergodic Markovian process with fast time.…

Probability · Mathematics 2007-05-23 R. Liptser

We consider the inclusion process on the complete graph with vanishing diffusivity, which leads to condensation of particles in the thermodynamic limit. Describing particle configurations in terms of size-biased and appropriately scaled…

Probability · Mathematics 2024-06-10 Paul Chleboun , Simon Gabriel , Stefan Grosskinsky

A diffusive system coupled to unequal boundary reservoirs reaches a non-equilibrium steady state. While the full-counting-statistics of current fluctuations in these states are well understood for generic systems, results for steady-state…

Statistical Mechanics · Physics 2026-01-29 Soumyabrata Saha , Tridib Sadhu

We consider interacting particle dynamics with Vicsek type interactions, and their macroscopic PDE limit, in the non-mean-field regime; that is, we consider the case in which each particle/agent in the system interacts only with a…

Pattern Formation and Solitons · Physics 2022-06-15 P. Buttà , B. Goddard , T. M. Hodgson , M. Ottobre , K. J. Painter

We consider certain random matrix eigenvalue dynamics, akin to Dyson Brownian motion, introduced by Rider and Valko. We show that from every initial condition, including ones involving coinciding coordinates, the dynamics, enhanced with…

Probability · Mathematics 2024-08-27 Theodoros Assiotis , Zahra Sadat Mirsajjadi

In this paper, we study multi-species stochastic interacting particle systems and their mean-field McKean-Vlasov partial differential equations (PDEs) in non-convex landscapes. We discuss the well-posedness of the multi-species SDE system,…

Probability · Mathematics 2025-07-11 Manh Hong Duong , Grigorios A. Pavliotis , Julian Tugaut

We propose a second order differential calculus to analyze the regularity and the stability properties of the distribution semigroup associated with McKean-Vlasov diffusions. This methodology provides second order Taylor type expansions…

Probability · Mathematics 2020-01-07 M Arnaudon , P del Moral

We consider fluctuations of the dissipated energy in nonlinear driven diffusive systems subject to bulk dissipation and boundary driving. With this aim, we extend the recently-introduced macroscopic fluctuation theory to nonlinear driven…

Statistical Mechanics · Physics 2013-10-29 P. I. Hurtado , A. Lasanta , A. Prados

We propose an explicit drift-randomised Milstein scheme for both McKean--Vlasov stochastic differential equations and associated high-dimensional interacting particle systems with common noise. By using a drift-randomisation step in space…

Probability · Mathematics 2023-06-19 Sani Biswas , Chaman Kumar , Neelima , Gonçalo dos Reis , Christoph Reisinger