Markov Paths, Loops and Fields [electronic resource] : cole d'tȨ de ProbabilitȨs de Saint-Flour XXXVIII 2008 / by Yves Le Jan.
Tipo de material:
TextoSeries Lecture Notes in Mathematics, 2026Editor: Berlin, Heidelberg : Springer Berlin Heidelberg, 2011Descripción: VIII, 124p. 9 illus. online resourceTipo de contenido: text Tipo de medio: computer Tipo de portador: online resourceISBN: 9783642212161Trabajos contenidos: SpringerLink (Online service)Tema(s): Mathematics | Potential theory (Mathematics) | Distribution (Probability theory) | Mathematics | Probability Theory and Stochastic Processes | Potential TheoryFormatos físicos adicionales: Sin títuloClasificación CDD: 519.2 Clasificación LoC:QA273.A1-274.9QA274-274.9Recursos en línea: de clik aquí para ver el libro electrónico 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.
ZDB-2-SMA
ZDB-2-LNM
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