Related papers: Random Problems in Mathematical Physics
$ $[This paper is a (self contained) chapter in a new book, Mathematics and Computation, whose draft is available on my homepage at https://www.math.ias.edu/avi/book ]. We survey some concrete interaction areas between computational…
These lecture notes provide a comprehensive, self-contained introduction to the analysis of Wishart matrix moments. This study may act as an introduction to some particular aspects of random matrix theory, or as a self-contained exposition…
These lectures introduce key concepts in probability and statistical inference at a level suitable for graduate students in particle physics. Our goal is to paint as vivid a picture as possible of the concepts covered.
We present a review of recent work on the statistical mechanics of non equilibrium processes based on the analysis of large deviations properties of microscopic systems. Stochastic lattice gases are non trivial models of such phenomena and…
Can machine learning help discover new mathematical structures? In this article we discuss an approach to doing this which one can call "mathematical data science". In this paradigm, one studies mathematical objects collectively rather than…
On the base of years of experience of working on the problem of the physical foundation of quantum mechanics the author offers principles of solving it. Under certain pressure of mathematical formalism there has raised a hypothesis of…
Contents: 1. Introduction 2. Bosonic propagators and random paths 3. Random surfaces and strings 4. Matrix models and two-dimensional quantum gravity 5. The mystery of $c > 1$ 6. Euclidean quantum gravity in $d > 2$ 7. Discussion
This celebratory article contains a personal and idiosyncratic selection of a few open problems in discrete probability theory. These include certain well known questions concerning Lorentz scatterers and self-avoiding walks, and also some…
This paper presents a general approach to linear stochastic processes driven by various random noises. Mathematically, such processes are described by linear stochastic differential equations of arbitrary order (the simplest non-trivial…
Random packings of objects of a particular shape are ubiquitous in science and engineering. However, such jammed matter states have eluded any systematic theoretical treatment due to the strong positional and orientational correlations…
The statistical physics approach to the number partioning problem, a classical NP-hard problem, is both simple and rewarding. Very basic notions and methods from statistical mechanics are enough to obtain analytical results for the phase…
Quantum dots pose a problem where one must confront three obstacles: randomness, interactions and finite size. Yet it is this confluence that allows one to make some theoretical advances by invoking three theoretical tools: Random Matrix…
The quantum diffusion of a particle in an initially localized state on a cyclic lattice with N sites is studied. Diffusion and reconstruction time are calculated. Strong differences are found for even or odd number of sites and the limit…
In this thesis I present a short review of ideas in quantum information theory. The first chapter contains introductory material, sketching the central ideas of probability and information theory. Quantum mechanics is presented at the level…
A variety of physical unknowables are discussed. Provable lack of physical omniscience, omnipredictability and omnipotence is derived by reduction to problems which are known to be recursively unsolvable. "Chaotic" symbolic dynamical…
A review is given of attempts to bridge the gap between everyday particle and nuclear physics - involving many quarks - and the basic underlying theory of QCD that can only be evaluated exactly for few quark systems. Even the latter…
This report summarizes some of the material that was presented by the author during the 2015 Les Houches Summerschool on "Random Matrices and Stochastic Processes". In these Lectures, various applications of Random Matrix Theory in modern…
We study diffusion processes in anomalous spacetimes regarded as models of quantum geometry. Several types of diffusion equation and their solutions are presented and the associated stochastic processes are identified. These results are…
Theoretical particle physicists continue to push the envelope in both high performance computing and in managing and analyzing large data sets. For example, the goals of sub-percent accuracy in predictions of quantum chromodynamics (QCD)…
We give a pedagogical introduction to a selection of recently discussed topics in nonequilibrium statistical mechanics, concentrating mostly on formal structures and on general principles. Part I contains an overview of the formalism of…