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We establish a connection between tagged particles and size-biased empirical processes in interacting particle systems, in analogy to classical results on the propagation of chaos. In a mean-field scaling limit, the evolution of the…

Probability · Mathematics 2026-03-03 Angeliki Koutsimpela , Stefan Grosskinsky

We derive a stochastic partial differential equation that describes the fluctuating behaviour of reaction-diffusion systems of N particles, undergoing Markovian, unary reactions. This generalises the work of Dean [J. Phys. A: Math. and…

Statistical Mechanics · Physics 2025-01-13 Richard E. Spinney , Richard G. Morris

Pathwise uniqueness for multi-dimensional stochastic McKean--Vlasov equation is established under moderate regularity conditions on the drift and diffusion coefficients. Both drift and diffusion depend on the marginal measure of the…

Probability · Mathematics 2023-01-02 Alexander Veretennikov

The aim of this paper is to investigate the large deviations for a class of slow-fast mean-field diffusions, which extends some existing results to the case where the laws of fast process are also involved in the slow component. Due to the…

Probability · Mathematics 2026-04-28 Wei Hong , Wei Liu , Shiyuan Yang

Many natural phenomena are effectively described by interacting particle systems, which can be modeled using either deterministic or stochastic differential equations (SDEs). In this study, we specifically investigate particle systems…

Analysis of PDEs · Mathematics 2024-04-01 Christian Kuehn , Carlos Pulido

A generic feature of systems with long-range interactions is the presence of {\it quasi-stationary} states with non-Gaussian single particle velocity distributions. For the case of the Hamiltonian Mean Field (HMF) model, we demonstrate that…

To sample from a given target distribution, Markov chain Monte Carlo (MCMC) sampling relies on constructing an ergodic Markov chain with the target distribution as its invariant measure. For any MCMC method, an important question is how to…

Probability · Mathematics 2023-08-15 Federica Milinanni , Pierre Nyquist

We consider a diffusion process on $\mathbb R^n$ and prove a large deviation principle for the empirical process in the joint limit in which the time window diverges and the noise vanishes. The corresponding rate function is given by the…

Probability · Mathematics 2024-12-31 Lorenzo Bertini , Davide Gabrielli , Claudio Landim

Large ensembles of stochastically evolving interacting particles describe phenomena in diverse fields including statistical physics, neuroscience, biology, and engineering. In such systems, the infinitesimal evolution of each particle…

Probability · Mathematics 2024-01-02 Kavita Ramanan

For a certain class of McKean-Vlasov processes, we introduce proxy processes that substitute the mean-field interaction with self-interaction, employing a weighted occupation measure. Our study encompasses two key achievements. First, we…

Probability · Mathematics 2025-11-04 Kai Du , Zhenjie Ren , Florin Suciu , Songbo Wang

Path-wise observables--functionals of stochastic trajectories--are at the heart of time-average statistical mechanics and are central to thermodynamic inequalities such as uncertainty relations, speed limits, and correlation-bounds. They…

Statistical Mechanics · Physics 2026-04-21 Lars Torbjørn Stutzer , Cai Dieball , Aljaž Godec

We study a system of N particles with logarithmic, Coulomb or Riesz pairwise interactions, confined by an external potential. We examine a microscopic quantity, the tagged empirical field, for which we prove a large deviation principle at…

Probability · Mathematics 2017-05-11 Thomas Leblé , Sylvia Serfaty

In this paper, we analyse the rate of convergence of a system of $N$ interacting particles with mean-field rank based interaction in the drift coefficient and constant diffusion coefficient. We first adapt arguments by Kolli and Shkolnikhov…

Probability · Mathematics 2020-11-13 Oumaima Bencheikh , Benjamin Jourdain

We give a new proof of the large deviation principle from the hydrodynamic limit for the Ginzberg-Landau model studied in Donsker and Varadhan (1989) using techniques from the theory of stochastic control and weak convergence methods. The…

Probability · Mathematics 2018-03-28 Sayan Banerjee , Amarjit Budhiraja , Michael Perlmutter

This paper investigates the estimation of the interaction function for a class of McKean-Vlasov stochastic differential equations. The estimation is based on observations of the associated particle system at time $T$, considering the…

Statistics Theory · Mathematics 2024-11-01 Chiara Amorino , Denis Belomestny , Vytautė Pilipauskaitė , Mark Podolskij , Shi-Yuan Zhou

In this paper, we develop a novel argument, the non-autonomous approximation method, to seek the asymptotic limits of the fully coupled multi-scale McKean-Vlasov stochastic systems with irregular coefficients, which, as summarized in…

Probability · Mathematics 2024-12-19 Yuewen Hou , Yun Li , Longjie Xie

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

McKean-Vlasov stochastic differential equations (MVSDEs) describe systems whose dynamics depend on both individual states and the population distribution, and they arise widely in neuroscience, finance, and epidemiology. In many…

Computation · Statistics 2026-01-21 Ning Ning , Amin Wu

We study the convergence of the empirical distribution associated with a system of interacting kinetic particles subject to independent Brownian forcing in a finite horizon setting, using some recent progress on kinetic non-linear partial…

Probability · Mathematics 2025-11-13 Carlo Bellingeri , Fabio Coppini

We consider two Ito equations that evolve on different time scales. The equations are fully coupled in the sense that all coefficients may depend on both the "slow" and the "fast" processes and the diffusion terms may be correlated. The…

Probability · Mathematics 2016-12-13 Anatolii A. Puhalskii