Markov paths, loops and fields : ecole dété de Probabilités de Saint-Flour XXXVIII-2008 /
Le Jan, Y. 1952-
Markov paths, loops and fields : ecole dété de Probabilités de Saint-Flour XXXVIII-2008 / Yves Le Jan. - Berlin ; Heidelberg : Springer-Verlag, ©2011. - 1 online resource (viii, 124 pages) : illustrations - Lecture notes in mathematics ; 2026 . - Lecture notes in mathematics (Springer-Verlag) ; 2026. .
Includes bibliographical references and index.
Symmetric Markov processes on finite spaces Loop measures Geodesic loops Poisson process of loops The Gaussian free field Energy variation and representations Decompositions Loop erasure and spanning trees Reflection positivity The case of general symmetric Markov processes. 1 -- 2 -- 3 -- 4 -- 5 -- 6 -- 7 -- 8 -- 9 -- 10 --
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.
9783642212161 3642212166 3642212158 9783642212154
10.1007/978-3-642-21216-1 doi
GBB1A6721 bnb
015861388 Uk 015885887 Uk
Markov processes.
Stochastic processes.
Processus de Markov.
Processus stochastiques.
Markov, Procesos de
Stochastic processes
Markov processes
Stochastic processes
QA274.7 / .L4 2011eb
519.2/33
Markov paths, loops and fields : ecole dété de Probabilités de Saint-Flour XXXVIII-2008 / Yves Le Jan. - Berlin ; Heidelberg : Springer-Verlag, ©2011. - 1 online resource (viii, 124 pages) : illustrations - Lecture notes in mathematics ; 2026 . - Lecture notes in mathematics (Springer-Verlag) ; 2026. .
Includes bibliographical references and index.
Symmetric Markov processes on finite spaces Loop measures Geodesic loops Poisson process of loops The Gaussian free field Energy variation and representations Decompositions Loop erasure and spanning trees Reflection positivity The case of general symmetric Markov processes. 1 -- 2 -- 3 -- 4 -- 5 -- 6 -- 7 -- 8 -- 9 -- 10 --
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.
9783642212161 3642212166 3642212158 9783642212154
10.1007/978-3-642-21216-1 doi
GBB1A6721 bnb
015861388 Uk 015885887 Uk
Markov processes.
Stochastic processes.
Processus de Markov.
Processus stochastiques.
Markov, Procesos de
Stochastic processes
Markov processes
Stochastic processes
QA274.7 / .L4 2011eb
519.2/33