LEADER 02678nam 2200613Ia 450 001 9910484809303321 005 20200520144314.0 010 $a9783642212161 010 $a3642212166 024 7 $a10.1007/978-3-642-21216-1 035 $a(CKB)2670000000096130 035 $a(SSID)ssj0000506048 035 $a(PQKBManifestationID)11331333 035 $a(PQKBTitleCode)TC0000506048 035 $a(PQKBWorkID)10513854 035 $a(PQKB)10934272 035 $a(DE-He213)978-3-642-21216-1 035 $a(MiAaPQ)EBC3066939 035 $z(PPN)258846747 035 $a(PPN)156307669 035 $a(EXLCZ)992670000000096130 100 $a20060525d2011 uy 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aMarkov paths, loops and fields $eecole dete de Probabilites de Saint-Flour XXXVIII-2008 /$fYves Le Jan 205 $a1st ed. 2011. 210 $aBerlin ;$aHeidelberg $cSpringer-Verlag$dc2011 215 $a1 online resource (VIII, 124 p. 9 illus.) 225 0 $aLecture notes in mathematics ;$v2026 300 $aBibliographic Level Mode of Issuance: Monograph 311 08$a9783642212154 311 08$a3642212158 320 $aIncludes bibliographical references and index. 327 $a1 Symmetric Markov processes on finite spaces -- 2 Loop measures -- 3 Geodesic loops -- 4 Poisson process of loops -- 5 The Gaussian free field -- 6 Energy variation and representations -- 7 Decompositions -- 8 Loop erasure and spanning trees -- 9 Reflection positivity -- 10 The case of general symmetric Markov processes. 330 $aThe purpose of these notes is to explore some simple relations between Markovian path and loop measures, the Poissonian ensembles of loops they determine, their occupation fields, uniform spanning trees, determinants, and Gaussian Markov fields such as the free field. These relations are first studied in complete generality for the finite discrete setting, then partly generalized to specific examples in infinite and continuous spaces. 410 0$aÉcole d'Été de Probabilités de Saint-Flour,$x0721-5363 ;$v2026 606 $aMarkov processes 606 $aStochastic processes 615 0$aMarkov processes. 615 0$aStochastic processes. 676 $a519.233 686 $a60J27$a60K35$a60J45$2msc 700 $aLe Jan$b Y$g(Yves),$f1952-$062931 712 12$aEcole d'e?te? de probabilite?s de Saint-Flour$d(38th :$f2008) 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910484809303321 996 $aMarkov paths, loops and fields$9261820 997 $aUNINA