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We study the behavior of solutions of mutually coupled equations in heterogeneous random graphs. Heterogeneity means that some equations receive many inputs whereas most of the equations are given only with a few connections. Starting from…

Dynamical Systems · Mathematics 2014-09-22 Eduardo Garibaldi , Tiago Pereira

We establish a process level large deviation principle for systems of interacting Bessel-like diffusion processes. By establishing weak uniqueness for the limiting non-local SDE of McKean-Vlasov type, we conclude that the latter describes…

Probability · Mathematics 2013-03-14 Tomoyuki Ichiba , Mykhaylo Shkolnikov

We study a mean field model of a complex network, focusing on edge and triangle densities. Our first result is the derivation of a variational characterization of the entropy density, compatible with the infinite node limit. We then…

Mathematical Physics · Physics 2015-06-12 Charles Radin , Lorenzo Sadun

We analyse the motion of a system of particles subjected a random force fluctuating in both space and time, and experiencing viscous damping. When the damping exceeds a certain threshold, the system undergoes a phase transition: the…

Disordered Systems and Neural Networks · Physics 2009-11-10 M. Wilkinson , B. Mehlig

We study an ensemble of strongly coupled electrons under continuous microwave irradiation interacting with a dissipative environment, a problem of relevance to the creation of highly polarized non-equilibrium states in nuclear magnetic…

Statistical Mechanics · Physics 2017-10-18 Alexander Karabanov , Dominic C. Rose , Walter Köckenberger , Juan P. Garrahan , Igor Lesanovsky

Nonlocal interactions are ubiquitous in nature and play a central role in many biological systems. In this paper, we perform a bifurcation analysis of a widely-applicable advection-diffusion model with nonlocal advection terms describing…

Analysis of PDEs · Mathematics 2023-05-25 Valeria Giunta , Thomas Hillen , Mark A. Lewis , Jonathan R. Potts

Focusing on stochastic systems arising in mean-field models, the systems under consideration belong to the class of switching diffusions, in which continuous dynamics and discrete events coexist and interact. The discrete events are modeled…

Probability · Mathematics 2019-01-18 Son L. Nguyen , George Yin , Tuan A. Hoang

We study diffusion-controlled processes in nonequilibrium steady states, where standard rate theory assumptions break down. Using transition path theory, we generalize the relations between reactive probability fluxes and measures of the…

Chemical Physics · Physics 2025-06-02 Seokjin Moon , David T. Limmer

We investigate the mean-field dynamics of stochastic McKean differential equations with heterogeneous particle interactions described by large network structures. To express a wide range of graphs, from dense to sparse structures, we…

Analysis of PDEs · Mathematics 2024-09-18 Christian Kuehn , Tobias Wöhrer

We consider a general framework for multi-type interacting particle systems on graphs, where particles move one at a time by random walk steps, different types may have different speeds, and may interact, possibly randomly, when they meet.…

Probability · Mathematics 2025-05-15 John Haslegrave , Peter Keevash

We consider the symmetric inclusion process on a general finite graph. Our main result establishes universal upper and lower bounds for the spectral gap of this interacting particle system in terms of the spectral gap of the random walk on…

Probability · Mathematics 2025-12-09 Seonwoo Kim , Federico Sau

By means of the principle of minimal sensitivity we generalize the microcanonical inflection-point analysis method by probing derivatives of the microcanonical entropy for signals of transitions in complex systems. A strategy of…

Statistical Mechanics · Physics 2018-05-04 Kai Qi , Michael Bachmann

This paper concerns the large deviations of a system of interacting particles on a random graph. There is no stochasticity, and the only sources of disorder are the random graph connections, and the initial condition. The average number of…

Probability · Mathematics 2021-03-08 James MacLaurin

In the nonlinear diffusion framework, stochastic processes of McKean-Vlasov type play an important role. In some cases they correspond to processes attracted by their own probability distribution: the so-called self-stabilizing processes.…

Probability · Mathematics 2014-09-04 Samuel Herrmann , Julian Tugaut

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

We introduce and analyse a continuum model for an interacting particle system of Vicsek type. The model is given by a non-linear kinetic partial differential equation (PDE) describing the time-evolution of the density $f_t$, in the single…

Mathematical Physics · Physics 2022-04-11 Paolo Buttà , Franco Flandoli , Michela Ottobre , Boguslaw Zegarlinski

Light propagation in an atomic medium whose coupled electronic levels form a diamond-configuration exhibits a critical dependence on the input conditions. In particular, the relative phase of the input fields gives rise to interference…

Atomic Physics · Physics 2009-11-11 S. Kajari-Schroeder , G. Morigi , S. Franke-Arnold , G. -L. Oppo

Nonreciprocal interactions, in which action-reaction symmetry is broken, provide a powerful route to collective dynamics that cannot be captured by equilibrium free-energy minimisation. Here, we introduce and analyse a two-species…

Statistical Mechanics · Physics 2026-05-11 Arjun R , Pratyush Prakash Patra , A. V. Anil Kumar

We study a system of $N$ interacting particles on $\bf{Z}$. The stochastic dynamics consists of two components: a free motion of each particle (independent random walks) and a pair-wise interaction between particles. The interaction belongs…

Probability · Mathematics 2011-10-25 A. Manita , V. Shcherbakov

We study parametrically driven quantum oscillators and show that, even for weak coupling between the oscillators, they can exhibit various many-body states with broken time-translation symmetry. In the quantum-coherent regime, the symmetry…

Mesoscale and Nanoscale Physics · Physics 2018-12-05 M. I. Dykman , Christoph Bruder , Niels Lörch , Yaxing Zhang