# Statistical Mechanics of Disordered Systems

@inproceedings{Bovier2006StatisticalMO, title={Statistical Mechanics of Disordered Systems}, author={Anton Bovier}, year={2006} }

Our mathematical understanding of the statistical mechanics of disordered systems is going through a period of stunning progress. This self-contained book is a graduate-level introduction for mathematicians and for physicists interested in the mathematical foundations of the field, and can be used as a textbook for a two-semester course on mathematical statistical mechanics. It assumes only some basic knowledge of classical physics; on the mathematics side, the reader should have a good working…

## 193 Citations

Classical and quantum out-of-equilibrium dynamics. Formalism and applications.

- Physics
- 2010

This thesis deals with the dynamics of systems coupled to an environment. We review the symmetries of the Martin-Siggia-Rose-Janssen-deDominicis formalism associated to Langevin equations. In…

Free energies of Boltzmann machines: self-averaging, annealed and replica symmetric approximations in the thermodynamic limit

- Computer ScienceJournal of Statistical Mechanics: Theory and Experiment
- 2019

This work focuses on a RBM characterized by digital couplings, and extends the Pastur–Shcherbina–Tirozzi method to prove the self-averaging property for the free energy, over its quenched expectation, in the infinite volume limit, then explicitly calculates its simplest approximation.

Interactions, Specifications, DLR probabilities and the Ruelle Operator in the One-Dimensional Lattice

- Mathematics
- 2014

In this paper, we describe several different meanings for the concept of Gibbs measure on the lattice $\mathbb{N}$ in the context of finite alphabets (or state space). We compare and analyze these…

A new parallel algorithm for simulation of spin glasses on scales of space-time periods of external fields with consideration of relaxation effects

- Physics
- 2012

We have investigated the statistical properties of an ensemble of disordered 1D spatial spin chains (SSCs) of finite length, placed in an external field, with consideration of relaxation effects. The…

Dynamical Gibbs-non-Gibbs transitions and Brownian percolation

- Mathematics
- 2014

This thesis deals with two different models in two different contexts.
The first part deals with dynamical Gibbs-non-Gibbs transitions.
Gibbs measures describe the equilibrium states of a system…

Statistical Properties of Ideal Ensemble of Disordered 1D Steric Spin-Chains

- Physics
- 2010

The statistical properties of ensemble of disordered 1D steric spin-chains (SSC) of various length are investigated. Using 1D spin-glass type classical Hamiltonian, the recurrent trigonometrical…

Mod-Gaussian Convergence and Its Applications for Models of Statistical Mechanics

- Mathematics, Computer Science
- 2014

This paper introduces the framework of L1-mod-Gaussian convergence in which the residue function is obtained as (up to a normalizing factor) the probability density of some sequences of random variables converging in law after a change of probability measure.

Phase transitions in nonlinear filtering

- Mathematics
- 2015

It has been established under very general conditions that the ergodic properties of Markov processes are inherited by their conditional distributions given partial information. While the existing…

Metastates in Mean-Field Models with Random External Fields Generated by Markov Chains

- Mathematics
- 2012

We extend the construction by Külske and Iacobelli of metastates in finite-state mean-field models in independent disorder to situations where the local disorder terms are a sample of an external…

Spin glass polynomial identities from entropic constraints

- Mathematics
- 2012

The core idea of stochastic stability is that thermodynamic observables must be robust under small (random) perturbations of the quenched Gibbs measure. Combining this idea with the cavity field…

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