Directed Polymers in Random Environments: École d'Été de Probabilités de Saint-Flour XLVI - 2016

by Francis Comets

Overview

Analyzing the phase transition from diffusive to localized behavior in a model of directed polymers in a random environment, this volume places particular emphasis on the localization phenomenon. The main questionis: What does the path of a random walk look like if rewards and penalties are spatially randomly distributed?This model, which provides a simplified version of stretched elastic chains pinned by random impurities, has attracted much research activity, but it (and its relatives) still holds many secrets, especially in high dimensions. It has non-gaussian scaling limits and it belongs to the so-called KPZ universality class when the space is one-dimensional. Adopting a Gibbsian approach, using general and powerful tools from probability theory, the discrete model is studied in full generality. Presenting the state-of-the art from different perspectives, and written in the form of a first course on the subject, this monograph is aimed at researchers in probability or statistical physics, but is also accessible to masters and Ph.D. students.

Product Details

ISBN-13:	9783319504872
Publisher:	Springer International Publishing
Publication date:	01/26/2017
Series:	Lecture Notes in Mathematics , #2175
Sold by:	Barnes & Noble
Format:	eBook
File size:	4 MB

Table of Contents

1 Introduction.- 2 Thermodynamics and Phase Transition.- 3 The martingale approach and the L² region.- 4 Lattice versus tree.- 5 Semimartingale approach and localization transition.- 6 Log-Gamma polymer model.- 7 Kardar-Parisi-Zhang equation and universality.- 8 Variational formulas.