Format:
Online-Ressource (VIII, 124p. 9 illus, digital)
ISBN:
9783642212161
Series Statement:
Lecture Notes in Mathematics 2026
Content:
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.
Content:
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.
Note:
Includes bibliographical references and index
Additional Edition:
ISBN 9783642212154
Additional Edition:
Buchausg. u.d.T. Le Jan, Yves, 1952 - Markov paths, loops and fields Heidelberg [u.a.] : Springer, 2011 ISBN 9783642212154
Additional Edition:
ISBN 3642212158
Language:
English
Subjects:
Mathematics
Keywords:
Markov-Kette
;
Markov-Kette
DOI:
10.1007/978-3-642-21216-1
URL:
Volltext
(lizenzpflichtig)
URL:
Volltext
(lizenzpflichtig)
Author information:
Le Jan, Yves 1952-
Bookmarklink