Large deviations of Markov processes (Part - 1) by Hugo Touchette

Large deviation theory in statistical physics: Recent advances and future challenges

DATE: 14 August 2017 to 13 October 2017
VENUE: Madhava Lecture Hall, ICTS, Bengaluru

Large deviation theory made its way into statistical physics as a mathematical framework for studying equilibrium systems, and is now increasingly used for studying nonequilibrium systems driven in steady states, quantum many-body systems, and disordered systems. Major breakthroughs in understanding these systems have resulted recently from using this theory and are establishing it as an integral part of theoretical statistical physics. In parallel, mathematicians have considerably developed this theory and applied it to a variety of situations and are now also actively working on numerical methods for simulating large deviations, often with a direct motivation to study physical systems.

The aim of this program is to bring together physicists and mathematicians working on large deviations to share their recent results, to engage in new collaborations, and to make progress on fundamental problems in statistical physics. The program will focus on three themes, which drive a large part of the research currently done in this field and in large deviation theory:

Nonequilibrium large deviations: Long-time and low-noise large deviations, escape problems, interacting particle models, fluctuation relations, macroscopic fluctuation theory, stochastic PDEs.
New frontiers of large deviation applications: Disordered systems, polymers, glassy systems, random matrices, quantum systems, random walks on graphs, complex networks, active matter, applications in biology.
Large deviation simulations: Cloning and splitting methods, importance sampling, free energy calculations, transition path sampling, action minimization and adaptive control methods.
The program will consist of short lectures by invited participants in the first half of each day, with the rest of the time available for discussions. There will also be some pedagogic lectures on a few advanced topics.

Special lecture series:

Entropy and large deviation theory based on entropy as a tool in the study of non-equilibrium dynamics of large systems with conserved quantities - S .R. S. Varadhan
Fluctuations and large deviations in nonequilibrium systems - B. Derrida
Large deviations in statistical physics - Hugo Touchette
Macroscopic fluctuation theory - Kirone Mallick
Random Matrix theory - Satya Majumdar
Large deviations for the Wiener Sausage - Frank den Hollander
Numerical approaches - Tony Lelievre
Large deviations in the context of heavy tails - Parthanil Roy


*Due to some unforeseen circumstances Prof. Srinivasa Varadhan will not be able to deliver the Srinivasa Ramanujan lecture series, therefore the lecture series stands cancelled
CONTACT US: ldt@icts.res.in

PROGRAM LINK: https://www.icts.res.in/program/ldt2017

Table of Contents (powered by https://videoken.com)
0:00:00 Start
0:00:11 Large deviations of Markov processes (Part - 1)
0:01:55 Outline
0:08:50 Process
0:18:09 Example
0:23:10 Reversibility
0:24:45 Non-hermitian operators
0:29:05 Differential operator
0:30:47 Eigen problem
0:37:36 Dynamical observables
0:41:18 Examples
0:49:35 Large deviation theory
1:00:08 Gartner Ellis Theorem
1:07:17 Functional Penon-Frobenius
1:14:09 Feynman - Kac
1:22:31 Spectral problem
1:26:30 Q&A

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