03042nam 22006015 450 99646666470331620200706210651.03-642-21216-610.1007/978-3-642-21216-1(CKB)2670000000096130(SSID)ssj0000506048(PQKBManifestationID)11331333(PQKBTitleCode)TC0000506048(PQKBWorkID)10513854(PQKB)10934272(DE-He213)978-3-642-21216-1(MiAaPQ)EBC3066939(PPN)258846747(PPN)156307669(EXLCZ)99267000000009613020110704d2011 u| 0engurnn|008mamaatxtccrMarkov Paths, Loops and Fields[electronic resource] École d'Été de Probabilités de Saint-Flour XXXVIII – 2008 /by Yves Le Jan1st ed. 2011.Berlin, Heidelberg :Springer Berlin Heidelberg :Imprint: Springer,2011.1 online resource (VIII, 124 p. 9 illus.) École d'Été de Probabilités de Saint-Flour,0721-5363 ;2026Bibliographic Level Mode of Issuance: Monograph3-642-21215-8 Includes bibliographical references and index.1 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.The 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.École d'Été de Probabilités de Saint-Flour,0721-5363 ;2026ProbabilitiesPotential theory (Mathematics)Probability Theory and Stochastic Processeshttps://scigraph.springernature.com/ontologies/product-market-codes/M27004Potential Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/M12163Probabilities.Potential theory (Mathematics).Probability Theory and Stochastic Processes.Potential Theory.519.23360J2760K3560J45mscLe Jan Yvesauthttp://id.loc.gov/vocabulary/relators/aut62931Ecole d'été de probabilités de Saint-Flour(38th :2008)BOOK996466664703316Markov paths, loops and fields261820UNISA