Related papers: Long-time dynamics of stochastic differential equa…
These are the notes for the 4.5-hour course with the same title that I delivered in August 2025 at the Les Houches summer school ``Exact Solvability and Quantum Information''. In these notes I pedagogically introduce the setting of…
These notes briefly summarize the lectures for the Summer School "Optimal transportation: Theory and applications" held by the second author in Grenoble during the week of June 22-26, 2009. Their goal is to describe some recent results on…
This is the written version of the supersymmetry lectures delivered at the 30th and 31st British Universities Summer Schools in Theoretical Elementary Particle Physics (BUSSTEPP) held in Oxford in September 2000 and in Manchester in…
This text grew out of notes I have used in teaching a one quarter course on integration at the advanced undergraduate level. My intent is to introduce the Lebesgue integral in a quick, and hopefully painless, way and then go on to…
This manuscript is an edited and refined version of the lecture script for a one-semester graduate course given originally at the PhD school in the Institute of Physics of Polish Academy of Sciences in the Spring/Summer semester of 2022.…
We present a reformulation of quantum mechanics in terms of probability measures and functions on a general classical sample space and in particular in terms of probability densities and functions on phase space. The basis of our proceeding…
This is a set of notes on phase transitions and critical phenomena prepared to accompany my lectures for the RHIC '97 summer school, held at Brookhaven from July 6 to 16, 1997.
Stochastic chains represent a wide and key variety of phenomena in many branches of science within the context of Information Theory and Thermodynamics. They are typically approached by a sequence of independent events or by a memoryless…
In these notes we present a pedagogical account of the population dynamics methods recently introduced to simulate large deviation functions of dynamical observables in and out of equilibrium. After a brief introduction on large deviation…
These lecture notes are based on an introductory course given by the author at the summer school "Noncommutative Algebraic Geometry" at MSRI in June 2012. The emphasis throughout is on examples to illustrate the many different facets of…
Making the most of multispectral image time-series is a promising but still relatively under-explored research direction because of the complexity of jointly analyzing spatial, spectral and temporal information. Capturing and characterizing…
Classical geometric mechanics, including the study of symmetries, Lagrangian and Hamiltonian mechanics, and the Hamilton-Jacobi theory, are founded on geometric structures such as jets, symplectic and contact ones. In this paper, we shall…
Most physical systems are modelled by an ordinary or a partial differential equation, like the n-body problem in celestial mechanics. In some cases, for example when studying the long term behaviour of the solar system or for complex…
This paper is the second in a series devoted to the study of Langevin systems subjected to a continuous time-delayed feedback control. The goal of our previous paper [Phys. Rev. E 91, 042114 (2015)] was to derive second-law-like…
This material complements David Chandler's Introduction to Modern Statistical Mechanics (Oxford University Press, 1987) in a graduate-level, one-semester course I teach in the Department of Chemistry at Duke University. Students enter this…
In this paper, we suggest a useful technique based on time change to be effective for dealing with the backward stochastic differential equations. We show the relation between the BSDEs with stochastic Lipschtz coeffecients and the ones…
This note presents reflections drawn from my recent experiences in teaching a course on mathematics and sustainability, with a particular emphasis on raising awareness of the topic and its broader implications. The lectures were structured…
This volume contains the papers accepted at the first DATE Friday Workshop on System-level Design Methods for Deep Learning on Heterogeneous Architectures (SLOHA 2021), held virtually on February 5, 2021. SLOHA 2021 was co-located with the…
These notes were written for the Cours Peccot given at the Coll\`ege de France in 2007.
A brief overview of hep-th/0201028 prepared for NATO Advanced Study Institute and EC Summer School on Progress in String, Field and Particle Theory, Cargese, Corsica, France, 25 June - 11 July 2002.