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We consider extended slow-fast systems of N interacting diffusions. The typical behavior of the empirical density is described by a nonlinear McKean-Vlasov equation depending on , the scaling parameter separating the time scale of the slow…

Analysis of PDEs · Mathematics 2021-08-09 Julien Barré , Cedric Bernardin , Raphaël Chétrite , Yash Chopra , Mauro Mariani

In this paper, we compute exactly the average density of a harmonically confined Riesz gas of $N$ particles for large $N$ in the presence of a hard wall. In this Riesz gas, the particles repel each other via a pairwise interaction that…

Statistical Mechanics · Physics 2021-10-25 Jitendra Kethepalli , Manas Kulkarni , Anupam Kundu , Satya N. Majumdar , David Mukamel , Gregory Schehr

We are dealing with the validity of a large deviation principle for a class of reaction-diffusion equations with polynomial nonlinearity, perturbed by a Gaussian random forcing. We are here interested in the regime where both the strength…

Probability · Mathematics 2017-05-02 Sandra Cerrai , Arnaud Debussche

We consider a system of stochastic interacting particles in $\mathbb{R}^d$ and we describe large deviations asymptotics in a joint mean-field and small-noise limit. Precisely, a large deviations principle (LDP) is established for the…

Probability · Mathematics 2020-11-17 Carlo Orrieri

We derive a systematic approach to the thermodynamics of quantum systems based on the underlying symmetry groups. We show that the entropy of a system can be described in terms of group-theoretical quantities that are largely independent of…

We study the statistical mechanics of classical two-dimensional "Coulomb gases" with general potential and arbitrary \beta, the inverse of the temperature. Such ensembles also correspond to random matrix models in some particular cases. The…

Mathematical Physics · Physics 2013-03-18 Etienne Sandier , Sylvia Serfaty

We study the distribution of the position of the rightmost particle $x_{\max}$ in a $N$-particle Riesz gas in one dimension confined in a harmonic trap. The particles interact via long-range repulsive potential, of the form $r^{-k}$ with…

Statistical Mechanics · Physics 2022-03-14 Jitendra Kethepalli , Manas Kulkarni , Anupam Kundu , Satya N. Majumdar , David Mukamel , Gregory Schehr

Using a Wigner function based approach, we study the Renyi entropy of a subsystem $A$ of a system of Bosons interacting with a local repulsive potential. The full system is assumed to be in thermal equilibrium at a temperature $T$ and…

Statistical Mechanics · Physics 2021-09-15 Ahana Chakraborty , Rajdeep Sensarma

We study equilibrium measures for Riesz gases in dimension $d$ with pairwise interaction kernel $|x-y|^{-s}$, subject to radially symmetric external fields. We characterise broad classes of confining potentials for which the equilibrium…

Mathematical Physics · Physics 2026-02-04 Sung-Soo Byun , Peter J. Forrester , Satya N. Majumdar , Gregory Schehr

This paper deals with Coulomb gases at an intermediate temperature regime. We define a local empirical field and identify a critical temperature scaling. We show that if the scaling of the temperature is supercritical, the local empirical…

Probability · Mathematics 2023-05-23 David Padilla-Garza

We study an inhomogeneous sparse random graph on [N] = {1, . . . , N } as introduced in a seminal paper by Bollobas, Janson and Riordan (2007): vertices have a type (here in a compact metric space S), and edges between different vertices…

Probability · Mathematics 2023-08-21 Luisa Andreis , Wolfgang König , Heide Langhammer , Robert I. A. Patterson

We investigate Sine$_\beta$, the universal point process arising as the thermodynamic limit of the microscopic scale behavior in the bulk of one-dimensional log-gases, or $\beta$-ensembles, at inverse temperature $\beta>0$. We adopt a…

Probability · Mathematics 2019-11-18 David Dereudre , Adrien Hardy , Thomas Leblé , Mylène Maïda

In this paper we prove a large deviation principle (LDP) for the empirical measure of a general system of mean-field interacting diffusions with singular drift (as the number of particles tends to infinity) and show convergence to the…

Probability · Mathematics 2020-07-02 Jasper Hoeksema , Thomas Holding , Mario Maurelli , Oliver Tse

A particle system with a single locally-conserved field (density) in a bounded interval with different densities maintained at the two endpoints of the interval is under study here. The particles interact in the bulk through a long range…

Probability · Mathematics 2012-10-02 Mustapha Mourragui , Enza Orlandi

The asymptotic behavior of the integrated density of states (IDS), \(N(E)\), is investigated for random Schr\"{o}dinger operators with a single-site potential \(V\) satisfying \(\mathrm{essinf}\, V = -\infty\). Under the assumption that the…

Mathematical Physics · Physics 2026-05-22 Yuta Nakagawa

We consider the quasi-deterministic behavior of systems with a large number, $n$, of deterministically interacting constituents. This work extends the results of a previous paper [J. Stat. Phys. 99:1225-1249 (2000)] to include vector-valued…

Statistical Mechanics · Physics 2021-04-28 Brian R. La Cour , William C. Schieve

We prove a large deviation principle for the finite dimensional marginals of the Gibbs distribution of the macroscopic `overlap'-parameters in the Hopfield model in the case where the number of random patterns, $M$, as a function of the…

Condensed Matter · Physics 2007-05-23 Anton Bovier , Véronique Gayrard

What does an Erdos-Renyi graph look like when a rare event happens? This paper answers this question when p is fixed and n tends to infinity by establishing a large deviation principle under an appropriate topology. The formulation and…

Probability · Mathematics 2011-04-05 Sourav Chatterjee , S. R. S. Varadhan

We develop a space-time large-deviation point of view on Gibbs-non-Gibbs transitions in spin systems subject to a stochastic spin-flip dynamics. Using the general theory for large deviations of functionals of Markov processes outlined in…

Probability · Mathematics 2015-03-17 Aernout van Enter , Roberto Fernández , Frank den Hollander , Frank Redig

We consider a lattice gas on the discrete d-dimensional torus $(\mathbb{Z}/N\mathbb{Z})^d$ with a generic translation invariant, finite range interaction satisfying a uniform strong mixing condition. The lattice gas performs a Kawasaki…

Mathematical Physics · Physics 2013-02-13 Lorenzo Bertini , Alessandra Faggionato , Davide Gabrielli