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＜電子ブック＞
Markov Paths, Loops and Fields : École d'Été de Probabilités de Saint-Flour XXXVIII – 2008 / by Yves Le Jan
(École d'Été de Probabilités de Saint-Flour ; 2026)

版	1st ed. 2011.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	2011
大きさ	VIII, 124 p. 9 illus : online resource
著者標目	*Le Jan, Yves author SpringerLink (Online service)
件　名	LCSH:Probabilities LCSH:Potential theory (Mathematics) FREE:Probability Theory FREE:Potential Theory
一般注記	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 HTTP:URL=https://doi.org/10.1007/978-3-642-21216-1

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