Random Explorations - Couverture souple

Lawler, Gregory F.

Couverture souple

ISBN 10 : 1470467666 ISBN 13 : 9781470467661

Editeur : American Mathematical Society, 2023

Synopsis

The title Random Explorations has two meanings. First, a few topics of advanced probability are deeply explored. Second, there is a recurring theme of analyzing a random object by exploring a random path.

This book is an outgrowth of lectures by the author in the University of Chicago Research Experiences for Undergraduate (REU) program in 2020. The idea of the course was to expose advanced undergraduates to ideas in probability research.

The book begins with Markov chains with an emphasis on transient or killed chains that have finite Green's function. This function, and its inverse called the Laplacian, is discussed next to relate two objects that arise in statistical physics, the loop-erased random walk (LERW) and the uniform spanning tree (UST). A modern approach is used including loop measures and soups. Understanding these approaches as the system size goes to infinity requires a deep understanding of the simple random walk so that is studied next, followed by a look at the infinite LERW and UST. Another model, the Gaussian free field (GFF), is introduced and related to loop measure. The emphasis in the book is on discrete models, but the final chapter gives an introduction to the continuous objects: Brownian motion, Brownian loop measures and soups, Schramm-Loewner evolution (SLE), and the continuous Gaussian free field. A number of exercises scattered throughout the text will help a serious reader gain better understanding of the material.

A propos du livre

À propos de l?auteur

Gregory F. Lawler, University of Chicago, IL.

Détails de l'édition

• Éditeur: American Mathematical Society
• Date d'édition: 2023
• Langue: anglais
• ISBN 10: 1470467666
• ISBN 13: 9781470467661
• Reliure: Broché
• Nombre de pages: 208
• Coordonnées du fabricant: non disponible
• Personne responsable: non disponible