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We give a sufficiently detailed account on the construction of marked Gibbs measures in the high temperature and low fugacity regime. This is proved for a wide class of underlying spaces and potentials such that stability and integrability…

Mathematical Physics · Physics 2007-05-23 Yuri Kondratiev , Tobias Kuna , Jose Luis Silva

We establish Gaussian limits for general measures induced by binomial and Poisson point processes in d-dimensional space. The limiting Gaussian field has a covariance functional which depends on the density of the point process. The general…

Probability · Mathematics 2007-05-23 Yu. Baryshnikov , J. E. Yukich

We study abelian anyons at the mean-field/almost-bosonic level, whose dynamics are governed by the Chern-Simons-Schr\"odinger system. We consider the dimensional reduction of this 2D model by introducing an anisotropic trapping potential,…

Analysis of PDEs · Mathematics 2025-11-06 Qiyun Yang

We study a mean-field model for a system of 2D abelian anyons, given by the dynamics of a Schr{\"o}dinger matter field coupled to a Chern-Simons gauge field. We derive an effective 1D equation by adding a strongly anisotropic trapping…

Analysis of PDEs · Mathematics 2026-01-27 Nicolas Rougerie , Qiyun Yang

In the case of smooth non-invertible maps which are hyperbolic on folded basic sets $\Lambda$, we give approximations for the Gibbs states (equilibrium measures) of arbitrary H\"{o}lder potentials, with the help of weighted sums of atomic…

Dynamical Systems · Mathematics 2010-06-21 Eugen Mihailescu

We obtain bounds on fluctuations of two entropy estimators for a class of one-dimensional Gibbs measures on the full shift. They are the consequence of a general exponential inequality for Lipschitz functions of n variables. The first…

Dynamical Systems · Mathematics 2015-05-27 J. -R. Chazottes , C. Maldonado

We prove the existence and the invariance of a Gibbs measure associated to the defocusing sub-quintic Nonlinear Schroedinger equations on the disc of the plane $\R^2$. We also prove an estimate giving some intuition to what may happen in 3…

Analysis of PDEs · Mathematics 2008-04-08 N. Tzvetkov

In this article we will describe a new construction for Gibbs measures for hyperbolic attractors generalizing the original construction of Sinai, Bowen and Ruelle of SRB measures. The classical construction of the SRB measure is based on…

Dynamical Systems · Mathematics 2022-04-19 David Parmenter , Mark Pollicott

We consider a general class of spin systems with potentially unbounded real-valued spins, defined via a single-site potential with super-Gaussian tails on general graphs, allowing for both short- and long-range interactions. This class…

Probability · Mathematics 2026-03-30 Christoforos Panagiotis , William Veitch

Given n independent Bernoulli(p) random variables X_i, i = 1, ..., n, representing the opinions of individuals connected by an underlying random k-regular graph G_n on {1, ..., n}, we show that when conditioned on an atypical empirical…

Probability · Mathematics 2026-03-03 I-Hsun Chen , Ivan Lee , Kavita Ramanan , Sarath Yasodharan

In a statistical mechanics model with unbounded spins, we prove uniqueness of the Gibbs measure under various assumptions on finite volume functional inequalities. We follow the approach of G. Royer (1999) and obtain uniqueness by showing…

Probability · Mathematics 2010-02-01 Pierre-André Zitt

We consider a class of many-body Hamiltonians composed of a free (kinetic) part and a multi-particle (potential) interaction with a compactness assumption on the latter part. We investigate the mean field limit of such quantum systems…

Mathematical Physics · Physics 2014-02-19 Boris Pawilowski , Quentin Liard

We build and analytically calculate the Generalised Gibbs Ensemble partition function of the integrable Soft Neumann Model. This is the model of a classical particle which is constrained to move, on average over the initial conditions, on…

Statistical Mechanics · Physics 2022-09-07 Damien Barbier , Leticia F. Cugliandolo , Gustavo S. Lozano , Nicolás Nessi

An integration by parts formula is derived for the first order differential operator corresponding to the action of translations on the space of locally finite simple configurations of infinitely many points on R^d. As reference measures,…

Mathematical Physics · Physics 2011-03-31 Florian Conrad , Tobias Kuna

We study thermodynamic formalism for topologically transitive partially hyperbolic systems in which the center-stable bundle satisfies a bounded expansion property, and show that every potential function satisfying the Bowen property has a…

Dynamical Systems · Mathematics 2020-12-24 Vaughn Climenhaga , Yakov Pesin , Agnieszka Zelerowicz

We show that under a low complexity condition on the gradient of a Hamiltonian, Gibbs distributions on the Boolean hypercube are approximate mixtures of product measures whose probability vectors are critical points of an associated…

Probability · Mathematics 2018-04-20 Ronen Eldan , Renan Gross

We study the thermodynamic formalism for generalized Gibbs measures, such as renormalization group transformations of Gibbs measures or joint measures of disordered spin systems. We first show existence of the relative entropy density and…

Probability · Mathematics 2007-05-23 Christof Kuelske , Arnaud Le Ny , Frank Redig

We investigate, in a fairly general setting, the limit of large volume equilibrium Gibbs measures for elasticity type Hamiltonians with clamped boundary conditions. The existence of a quasiconvex free energy, forming the large deviations…

Mathematical Physics · Physics 2012-06-27 Roman Kotecký , Stephan Luckhaus

In this work the Klein-Gordon (KG) equation for a complex scalar field with U(1) symmetry endowed in a mexican-hat scalar field potential with thermal and electromagnetic contributions is written as a Gross-Pitaevskii (GP)-like equation.…

Quantum Gases · Physics 2017-08-10 Tonatiuh Matos , Elías Castellanos , Abril Suárez

We consider the one dimensional cubic nonlinear Schr{\"o}dinger equation with trapping potential behaving like |x| s (s > 1) at infinity. We construct Gibbs measures associated to the equation and prove that the Cauchy problem is globally…

Analysis of PDEs · Mathematics 2023-02-07 Van Duong Dinh , Nicolas Rougerie