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Record Nr. |
UNINA9910484809303321 |
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Autore |
Le Jan Yves |
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Titolo |
Markov Paths, Loops and Fields [[electronic resource] ] : École d'Été de Probabilités de Saint-Flour XXXVIII – 2008 / / by Yves Le Jan |
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Pubbl/distr/stampa |
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Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2011 |
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ISBN |
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Edizione |
[1st ed. 2011.] |
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Descrizione fisica |
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1 online resource (VIII, 124 p. 9 illus.) |
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Collana |
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École d'Été de Probabilités de Saint-Flour, , 0721-5363 ; ; 2026 |
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Classificazione |
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Disciplina |
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Soggetti |
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Probabilities |
Potential theory (Mathematics) |
Probability Theory and Stochastic Processes |
Potential Theory |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Bibliographic Level Mode of Issuance: Monograph |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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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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Sommario/riassunto |
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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. |
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