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Markov Paths, Loops and Fields : École d'Été de Probabilités de Saint-Flour XXXVIII – 2008 / by Yves Le Jan

By: Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: SpringerLink Bücher | Lecture notes in mathematics ; 2026Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2011Description: Online-Ressource (VIII, 124p. 9 illus, digital)ISBN:
  • 9783642212161
Subject(s): Additional physical formats: 9783642212154 | Buchausg. u.d.T.: Markov paths, loops and fields. Heidelberg [u.a.] : Springer, 2011. VIII, 124 S.DDC classification:
  • 519.233
  • 519.2
MSC: MSC: *60-02 | 60J27 | 60J45 | 60J80 | 60K35RVK: RVK: SI 850LOC classification:
  • QA273.A1-274.9 QA274-274.9
  • QA274.7
DOI: DOI: 10.1007/978-3-642-21216-1Online resources: Summary: 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.PPN: PPN: 1651001723Package identifier: Produktsigel: ZDB-2-SEB | ZDB-2-SXMS | ZDB-2-LNM | ZDB-2-SMA
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