Markov Paths, Loops and Fields

Ecole d'Ete de Probabilites de Saint-Flour XXXVIII - 2008

By: Yves Le Jan

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eText | 6 July 2011

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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 fre 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.