Markov Paths, Loops and Fields
École d'Été de Probabilités de Saint-Flour XXXVIII - 2008
(Sprache: Englisch)
Based on lecture notes, this book explores 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.
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Based on lecture notes, this book explores 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.
Klappentext zu „Markov Paths, Loops and Fields “
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.
Inhaltsverzeichnis zu „Markov Paths, Loops and Fields “
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.
Bibliographische Angaben
- Autor: Yves Le Jan
- 2011, 2011, VIII, 124 Seiten, Maße: 15,5 x 23,5 cm, Kartoniert (TB), Englisch
- Verlag: Springer, Berlin
- ISBN-10: 3642212158
- ISBN-13: 9783642212154
- Erscheinungsdatum: 06.07.2011
Sprache:
Englisch
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