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The dispersion of a diffusive scalar in a fluid flowing through a network has many applications including to biological flows, porous media, water supply and urban pollution. Motivated by this, we develop a large-deviation theory that…

Fluid Dynamics · Physics 2016-09-14 Alexandra Tzella , Jacques Vanneste

We use a weak Gibbs property and a weak form of specification to derive level-2 large deviations principles for symbolic systems equipped with a large class of reference measures. This has applications to a broad class of symbolic systems,…

Dynamical Systems · Mathematics 2017-10-25 Vaughn Climenhaga , Daniel J. Thompson , Kenichiro Yamamoto

The aim of this paper is to investigate the large deviations for a class of slow-fast mean-field diffusions, which extends some existing results to the case where the laws of fast process are also involved in the slow component. Due to the…

Probability · Mathematics 2026-04-28 Wei Hong , Wei Liu , Shiyuan Yang

This document consists of lecture notes for a graduate course, which focuses on the relations between Information Theory and Statistical Physics. The course is aimed at EE graduate students in the area of Communications and Information…

Information Theory · Computer Science 2010-06-09 Neri Merhav

The goal of this introduction to symmetries is to present some general ideas, to outline the fundamental concepts and results of the subject and to situate a bit the following lectures of this school. [These notes represent the write-up of…

High Energy Physics - Theory · Physics 2007-05-23 Francois Gieres

Thermodynamics of trajectories promises to make possible the thorough analysis of the dynamical properties of an open quantum system, a sought-after goal in modern physics. Unfortunately, calculation of the relevant quantities presents…

Quantum Physics · Physics 2016-06-14 Simon Pigeon , André Xuereb

In the standard formulation of the occupancy problem one considers the distribution of r balls in n cells, with each ball assigned independently to a given cell with probability 1/n. Although closed form expressions can be given for the…

Probability · Mathematics 2007-05-23 Paul Dupuis , Carl Nuzman , Phil Whiting

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

These lecture notes introduce some topics of classical statistical physics, particularly those that are relevant for neural networks and deep learning. Statistical physics is treated as a branch of probability theory or statistics, with the…

Disordered Systems and Neural Networks · Physics 2026-05-12 Olaf Hohm

These are lecture notes written at the University of Zurich during spring 2014 and spring 2015. The first part of the notes gives an introduction to probability theory. It explains the notion of random events and random variables,…

Probability · Mathematics 2020-11-02 Nima Moshayedi

These are lecture notes for various Summer and Winter schools that I have given. The notes describe the methodology called Variational Modelling, and focus on the application to the modelling of gradient-flow systems. I describe the…

Mathematical Physics · Physics 2014-02-11 Mark A. Peletier

The standard Large Deviation Theory (LDT) is mathematically illustrated by the Boltzmann-Gibbs factor which describes the thermal equilibrium of short-range-interacting many-body Hamiltonian systems, the velocity distribution of which is…

Statistical Mechanics · Physics 2021-12-24 Ugur Tirnakli , Constantino Tsallis , Nihat Ay

We obtain large deviations theorems for nonconventional sums with underlying process being a Markov process satisfying the Doeblin condition or a dynamical system such as subshift of finite type or hyperbolic or expanding transformation.

Probability · Mathematics 2013-02-21 Yuri Kifer , S. R. S. Varadhan

These brief lecture notes are intended mainly for undergraduate students in engineering or physics or mathematics who have met or will soon be meeting the Dirac delta function and some other objects related to it. These students might have…

Classical Analysis and ODEs · Mathematics 2018-10-19 Michael Cwikel

This collection of studies on new physics at the LHC constitutes the report of the supersymmetry working group at the Workshop `Physics at TeV Colliders', Les Houches, France, 2007. They cover the wide spectrum of phenomenology in the LHC…

When teaching and discussing statistical assumptions, our focus is oftentimes placed on how to test and address potential violations rather than the effects of violating assumptions on the estimates produced by our statistical models. The…

Methodology · Statistics 2022-06-14 Ian A Silver

This is the write-up of the talk I gave at the 23rd International Symposium on Mathematical Programming (ISMP) in Bordeaux, France, July 6th, 2018. The talk was a general overview of the state of the art of time-varying, mainly convex,…

Optimization and Control · Mathematics 2018-08-02 Andrea Simonetto

We present an efficient approach, based on a number-conditioned master equation, for large-deviation analysis in mesoscopic transports. Beyond the conventional full-counting-statistics study, the large-deviation approach encodes complete…

Mesoscale and Nanoscale Physics · Physics 2011-09-30 Jun Li , Yu Liu , Jing Ping , Shu-Shen Li , Xin-Qi Li , YiJing Yan

We consider a finite collection of independent Hermitian heavy-tailed random matrices of growing dimension. Our model includes the L\'evy matrices proposed by Bouchaud and Cizeau, as well as sparse random matrices with O(1) non-zero entries…

Probability · Mathematics 2024-09-24 Charles Bordenave , Alice Guionnet , Camille Male