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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

The large deviation principle is proved for a class of $L^2$-valued processes that arise from the coarse-graining of a random field. Coarse-grained processes of this kind form the basis of the analysis of local mean-field models in…

Mathematical Physics · Physics 2007-05-23 R. S. Ellis , K. Haven , B. Turkington

We prove a large deviation principle for the expectation of macroscopic observables in quantum (and classical) Gibbs states. Our proof is based on Ruelle-Lanford functions and direct subadditivity arguments, as in the classical case,…

Mathematical Physics · Physics 2010-09-24 Yoshiko Ogata , Luc Rey-Bellet

We compute the probability of positive large deviations of the free energy per spin in mean-field Spin-Glass models. The probability vanishes in the thermodynamic limit as $P(\Delta f) \propto \exp[-N^2 L_2(\Delta f)]$. For the…

Disordered Systems and Neural Networks · Physics 2012-10-31 Giorgio Parisi , Tommaso Rizzo

Generalized Large deviation principles was developed for Colombeau-Ito SDE with a random coefficients. We is significantly expand the classical theory of large deviations for randomly perturbed dynamical systems developed by Freidlin and…

Mathematical Physics · Physics 2024-06-03 Jaykov Foukzon

Using an effective Hamiltonian including the Zeeman and internal interactions, we describe the quantum theory of magnetization dynamics when the spin system evolves non-adiabatically and out of equilibrium. The Lewis-Riesenfeld dynamical…

Other Condensed Matter · Physics 2008-11-26 F. M. Saradzhev , F. C. Khanna , Sang Pyo Kim , M. de Montigny

We derive moderate deviation principles for the trajectory of the empirical magnetization of the standard Curie-Weiss model via a general analytic approach based on convergence of generators and uniqueness of viscosity solutions for…

Probability · Mathematics 2017-10-13 Francesca Collet , Richard Kraaij

We derive a large deviation principle for random permutations induced by probability measures of the unit square, called permutons. These permutations are called $\mu$-random permutations. We also introduce and study a new general class of…

Probability · Mathematics 2023-04-04 Jacopo Borga , Sayan Das , Sumit Mukherjee , Peter Winkler

We consider the moment space $\mathcal{M}_n^{K}$ corresponding to $p \times p$ complex matrix measures defined on $K$ ($K=[0,1]$ or $K=\D$). We endow this set with the uniform law. We are mainly interested in large deviations principles…

Probability · Mathematics 2011-10-17 Fabrice Gamboa , Jan Nagel , Alain Rouault , Jens Wagener

This work continues the analysis of large deviations for randomly connected neural networks models of the brain. The originality of the model relies on the fact that the directed impact of one particle onto another depends on the state of…

Probability · Mathematics 2017-01-05 Tanguy Cabana , Jonathan Touboul

In this paper, we introduce a mathematical apparatus that is relevant for understanding a dynamical system with small random perturbations and coupled with the so-called transmutation process -- where the latter jumps from one mode to…

Dynamical Systems · Mathematics 2017-09-15 Getachew K. Befekadu

We present a large deviations theory of the spin-spin correlation functions in the Random Field Ising Model on the Bethe lattice, both at finite and zero temperature. Rare events of atypically correlated variables are particularly important…

Disordered Systems and Neural Networks · Physics 2014-07-02 Flaviano Morone , Giorgio Parisi , Federico Ricci-Tersenghi

We establish a large deviation principle for a reflected Poisson driven SDE. Our motivation is to study in a forthcoming paper the problem of exit of such a process from the basin of attraction of a locally stable equilibrium associated…

Probability · Mathematics 2020-03-09 Etienne Pardoux , Brice Samegni-Kepgnou

In contrast to the study of Langevin equations in a homogeneous environment in the literature, the study on Langevin equations in randomly-varying environments is relatively scarce. Almost all the existing works require random environments…

Probability · Mathematics 2021-08-25 Nhu N. Nguyen , George Yin

We analyse large deviations of the magnetisation in two models of growing clusters. The models have symmetry-breaking transitions, so the typical magnetisation of a growing cluster may be either positive or negative, with equal probability.…

Statistical Mechanics · Physics 2019-07-29 Robert L. Jack

In this paper, we present a large-deviation theory developed for functionals of canonical Gibbs processes, i.e., Gibbs processes with respect to the binomial point process. We study the regime of a fixed intensity in a sequence of…

Probability · Mathematics 2025-05-29 Christian Hirsch , Martina Petráková

This paper deals with rare events in a general {interacting gas} at high temperature, by means of Large Deviations Principles. The main result is an LDP for the tagged empirical field, which features the competition of an energy term and an…

Probability · Mathematics 2025-06-17 David Padilla-Garza

We consider large random trees under Gibbs distributions and prove a Large Deviation Principle (LDP) for the distribution of degrees of vertices of the tree. The LDP rate function is given explicitly. An immediate consequence is a Law of…

Probability · Mathematics 2009-11-13 Yuri Bakhtin , Christine Heitsch

The Large Deviations Principle (LDP) is verified for a homogeneous diffusion process with respect to a Brownian motion $B_t$, $$ X^\eps_t=x_0+\int_0^tb(X^\eps_s)ds+ \eps\int_0^t\sigma(X^\eps_s)dB_s, $$ where $b(x)$ and $\sigma(x)$ are are…

Probability · Mathematics 2011-08-24 P. Chigansky , R. Liptser

Starting with the large deviation principle (LDP) for the Erd\H{o}s-R\'enyi binomial random graph $\mathcal{G}(n,p)$ (edge indicators are i.i.d.), due to Chatterjee and Varadhan (2011), we derive the LDP for the uniform random graph…

Probability · Mathematics 2018-05-01 Amir Dembo , Eyal Lubetzky