Lecture notes on the Gaussian free field / Wendelin Werner, Ellen Powell.

Format:

Book

Author/Creator:

Werner, Wendelin, 1968- author.

Powell, Ellen, (Mathematician), author.

Contributor:

Société mathématique de France, issuing body.

Series:

Collection SMF. Cours spécialisés ; no 28.

Collection SMF. Cours spécialisés, 1284-6090 ; 28

Language:

English

French

Subjects (All):

Gaussian processes.

Brownian motion processes.

Physical Description:

vi, 171 pages : illustrations ; 25 cm.

Place of Publication:

Paris : Société mathématique de France, [2021]

Language Note:

Text in English; abstract in English and French.

Summary:

"The Gaussian Free Field (GFF) in the continuum appears to be the natural generalisation of Brownian motion, when one replaces time by a multidimensional continuous parameter. While Brownian motion can be viewed as the most natural random real-valued function defined on R+ with B(0)=0, the GFF in a domain D of Rd for d≥2 is a natural random real-valued generalised function defined on D with zero boundary conditions on ∂D. In particular, it is not a random continuous function.The goal of these lecture notes is to describe some aspects of the continuum GFF and of its discrete counterpart defined on lattices, with the aim of providing a gentle self-contained introduction to some recent developments on this topic, such as the relation between the continuum GFF, Brownian loop-soups and the Conformal Loop Ensembles CLE4.This is an updated and expanded version of the notes written by the first author (Wendelin Werner) for graduate courses at ETH Zürich (Swiss Federal Institute of Technology in Zürich) in 2014 and 2018. It has benefited from the comments and corrections of students, as well as of a referee. The exercises that are interspersed in the first half of these notes mostly originate from the exercise sheets prepared by the second author (Ellen Powell) for this course in 2018." - publisher

Contents:

Warm-up

The discrete GFF

Loop-soups and the discrete GFF

The continuum GFF

The Markov property and local sets in the continuum

Topography of the continuum Gaussian Free Field

Quick review of further related results.

Notes:

Includes bibliographical refeferences (pages 167-171).

ISBN:

9782856299524

2856299520

OCLC:

1340692455