TY  - BOOK
AU  - Sznitman,Alain-Sol
AU  - Sznitman,Alain-Sol
TI  - Topics in Occupation Times and Gaussian Free Fields
T2  - Zurich Lectures in Advanced Mathematics (ZLAM)
SN  - 9783037196090
PY  - 2012///
CY  - Zuerich, Switzerland
PB  - European Mathematical Society Publishing House
KW  - Probability & statistics
KW  - bicssc
KW  - Probability theory and stochastic processes
KW  - msc
KW  - Statistical mechanics, structure of matter
N1  - Restricted to subscribers
N2  - This book grew out of a graduate course at ETH Zurich during the Spring term  2011. It explores various links between such notions as occupation times of  Markov chains, Gaussian free fields, Poisson point processes of Markovian loops,  and random interlacements, which have been the object of intensive research  over the last few years. These notions are developed in the convenient set-up  of finite weighted graphs endowed with killing measures.    The book first discusses elements of continuous-time Markov chains, Dirichlet  forms, potential theory, together with some consequences for Gaussian free  fields. Next, isomorphism theorems and generalized Ray-Knight theorems,  which relate occupation times of Markov chains to Gaussian free fields, are pre-  sented. Markovian loops are constructed and some of their key properties  derived. The field of occupation times of Poisson point processes of Markovian  loops is investigated. Of special interest are its connection to the Gaussian free  field, and a formula of Symanzik. Finally, links between random interlacements  and Markovian loops are discussed, and some further connections with  Gaussian free fields are mentioned
UR  - https://doi.org/10.4171/109
UR  - http://www.ems-ph.org/img/books/sznitman_mini.jpg
ER  -