LEADER 02599nam  22004095a 450 
001 9910151927603321
005 20120503234500.0
010   $a3-03719-609-2
024 70$a10.4171/109
035   $a(CKB)3710000000953882
035   $a(CH-001817-3)149-120503
035   $a(PPN)178156094
035   $a(EXLCZ)993710000000953882
100   $a20120503j20120511  fy             0
101 0 $aeng
135   $aurnn|mmmmamaa
181   $ctxt$2rdacontent
182   $cc$2rdamedia
183   $acr$2rdacarrier
200 10$aTopics in Occupation Times and Gaussian Free Fields$b[electronic resource] /$fAlain-Sol Sznitman
210 3 $aZuerich, Switzerland $cEuropean Mathematical Society Publishing House$d2012
215   $a1 online resource (121 pages)
225 0 $aZurich Lectures in Advanced Mathematics (ZLAM)
330   $aThis 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.
606   $aProbability & statistics$2bicssc
606   $aProbability theory and stochastic processes$2msc
606   $aStatistical mechanics, structure of matter$2msc
615 07$aProbability & statistics
615 07$aProbability theory and stochastic processes
615 07$aStatistical mechanics, structure of matter
686   $a60-xx$a82-xx$2msc
700   $aSznitman$b Alain-Sol$0552964
801  0$bch0018173
906   $aBOOK
912   $a9910151927603321
996   $aTopics in Occupation Times and Gaussian Free Fields$92564451
997   $aUNINA