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035   $a(DE-He213)978-3-642-21216-1
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100   $a20110704d2011      u|             0
101 0 $aeng
135   $aurnn|008mamaa
181   $ctxt
182   $cc
183   $acr
200 10$aMarkov Paths, Loops and Fields$b[electronic resource] $eÉcole d'Été de Probabilités de Saint-Flour XXXVIII ? 2008 /$fby Yves Le Jan
205   $a1st ed. 2011.
210  1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2011.
215   $a1 online resource (VIII, 124 p. 9 illus.) 
225 1 $aÉcole d'Été de Probabilités de Saint-Flour,$x0721-5363 ;$v2026
300   $aBibliographic Level Mode of Issuance: Monograph
311   $a3-642-21215-8 
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   $aProbabilities
606   $aPotential theory (Mathematics)
606   $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004
606   $aPotential Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M12163
615  0$aProbabilities.
615  0$aPotential theory (Mathematics).
615 14$aProbability Theory and Stochastic Processes.
615 24$aPotential Theory.
676   $a519.233
686   $a60J27$a60K35$a60J45$2msc
700   $aLe Jan$b Yves$4aut$4http://id.loc.gov/vocabulary/relators/aut$062931
712 12$aEcole d'e?te? de probabilite?s de Saint-Flour$d(38th :$f2008)
906   $aBOOK
912   $a9910484809303321
996   $aMarkov paths, loops and fields$9261820
997   $aUNINA