Markov Paths, Loops and Fields École d'Été de Probabilités de Saint-Flour XXXVIII - 2008 /

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 studi...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Le Jan, Yves (Autor)
Autor Corporativo: SpringerLink (Online service)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2011.
Edición:1st ed. 2011.
Colección:École d'Été de Probabilités de Saint-Flour ; 2026
Temas:
Probabilities.
Potential theory (Mathematics).
Probability Theory.
Potential Theory.
Acceso en línea:Texto Completo
Tabla de Contenidos:
  • 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.

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