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Markov paths, loops and fields : ecole dété de Probabilités de Saint-Flour XXXVIII-2008 / Yves Le Jan.

By: Material type: TextTextSeries: Lecture notes in mathematics (Springer-Verlag) ; 2026.Publication details: Berlin ; Heidelberg : Springer-Verlag, ©2011.Description: 1 online resource (viii, 124 pages) : illustrationsContent type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9783642212161
  • 3642212166
  • 3642212158
  • 9783642212154
Subject(s): Additional physical formats: Print version:: Markov paths, loops and fields.DDC classification:
  • 519.2/33 23
LOC classification:
  • QA274.7 .L4 2011eb
Online resources:
Contents:
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.
Summary: 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.
Holdings
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Includes bibliographical references and index.

Print version record.

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.

English.

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