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We study effects of independent white noise on synchronization phenomena in ensembles of coupled limit cycle oscillators with different native frequencies. We consider a simple model where the ensemble consists of two inter-connected…

Statistical Mechanics · Physics 2011-01-04 K. Okumura , A. Ichiki , M. Shiino

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

In this paper, we study weakly interacting diffusion processes on random graphs. Our main focus is on the properties of the mean-field limit and, in particular, on the nonuniqueness and bifurcation structure of stationary states. By…

Dynamical Systems · Mathematics 2025-11-03 Benedetta Bertoli , Grigorios A. Pavliotis , Niccolò Zagli

A mean-field approach (MFA) is proposed for the analysis of orientational order in a two-dimensional system of stochastic self-propelled particles interacting by local velocity alignment mechanism. The treatment is applied to the cases of…

Statistical Mechanics · Physics 2009-11-13 Fernando Peruani , Andreas Deutsch , Markus Baer

We study the mean-field theory, and the properties of fluctuations, in an out of equilibrium Bose-Fermi system, across the transition to a quantum condensed phase. The system is driven out of equilibrium by coupling to multiple baths, which…

Other Condensed Matter · Physics 2007-09-11 M. H. Szymanska , J. Keeling , P. B. Littlewood

The weak coupling limit for a quantum system, with discrete energy spectrum, coupled to a Bose reservoir with the most general linear interaction is considered: under this limit we have a quantum noise processes substituting for the field.…

Mathematical Physics · Physics 2013-03-05 L. Accardi , J. Gough , Y. G. Lu

In this paper, we study the non-linear diffusion equation associated with a particle system where the common drift depends on the rate of absorption of particles at a boundary. We provide an interpretation as a structural credit risk model…

Numerical Analysis · Mathematics 2018-08-28 Alexander Lipton , Vadim Kaushansky , Christoph Reisinger

This paper establishes an indirect approximation theorem for the most probable transition pathway of a stochastic interacting particle system in the mean-field framework. This paper studied the problem of indirect approximation of the most…

Dynamical Systems · Mathematics 2026-05-27 Jianyu Chen , Ting Gao , Galina Strelkova , Jinqiao Duan

The paper has two objectives: proving that the rate of convergence in distribution for mean-field models in CLT regime is $N^{-1/2}$, and obtaining explicit expressions for the infinitesimal generators of two types of measure-valued Markov…

Probability · Mathematics 2025-02-05 Xavier Erny

We extend the celebrated Rothschild and Stiglitz (1970) definition of Mean-Preserving Spreads to a dynamic framework. We adapt the original integral conditions to transition probability densities, and give sufficient conditions for their…

Probability · Mathematics 2018-03-26 Jean-Louis Arcand , Max-Olivier Hongler , Daniele Rinaldo

We discuss recent results obtained for the Hamiltonian Mean Field model. The model describes a system of N fully-coupled particles in one dimension and shows a second-order phase transition from a clustered phase to a homogeneous one when…

Statistical Mechanics · Physics 2009-10-31 V. Latora , A. Rapisarda , S. Ruffo

Relationships between inter-cluster synchronization phenomena and external noise are studied on the basis of noise level-free analysis. We consider a mean-field model of ensembles of coupled limit cycle oscillators with two natural…

Statistical Mechanics · Physics 2011-01-04 K. Okumura , A. Ichiki , M. Shiino

We establish the local asymptotic normality (LAN) property for estimating a multidimensional parameter in the drift of a system of $N$ interacting particles observed over a fixed time horizon in a mean-field regime $N \rightarrow \infty$.…

Statistics Theory · Mathematics 2022-05-13 Laetitia Della Maestra , Marc Hoffmann

A new non-conservative stochastic reaction-diffusion system in which two families of random walks in two adjacent domains interact near the interface is introduced and studied in this paper. Such a system can be used to model the transport…

Probability · Mathematics 2021-01-12 Zhen-Qing Chen , Wai-Tong Louis Fan

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

Inferring dynamical models from low-resolution temporal data continues to be a significant challenge in biophysics, especially within transcriptomics, where separating molecular programs from noise remains an important open problem. We…

Machine Learning · Computer Science 2023-10-05 Victor Chardès , Suryanarayana Maddu , Michael J. Shelley

The one-dimensional motion of any number $\cN$ of particles in the field of many independent waves (with strong spatial correlation) is formulated as a second-order system of stochastic differential equations, driven by two Wiener…

Probability · Mathematics 2014-04-10 Yves Elskens , Etienne Pardoux

Nucleon transfer in symmetric heavy-ion reactions at energies below the Coulomb barrier is investigated in the framework of a microscopic stochastic mean-field theory. While mean-field alone is known to significantly underpredict the…

Nuclear Theory · Physics 2015-05-13 Kouhei Washiyama , Sakir Ayik , Denis Lacroix

The usual Langevin approach to describe systems driven by noise fails to describe the long time behavior of systems with multiple attractors. The solution of the associated linear Fokker-Planck equation is always unique, even though it…

Statistical Mechanics · Physics 2017-06-20 M. Morillo , J. M. Casado

We consider a system consisting of $n$ particles, moving forward in jumps on the real line. System state is the empirical distribution of particle locations. Each particle ``jumps forward'' at some time points, with the instantaneous rate…

Probability · Mathematics 2023-03-03 Alexander Stolyar