TY  - BOOK
AU  - Le Jan,Yves
ED  - SpringerLink (Online service)
TI  - Markov Paths, Loops and Fields: École d'Été de Probabilités de Saint-Flour XXXVIII – 2008 
T2  - Lecture Notes in Mathematics,
SN  - 9783642212161
AV  - QA273.A1-274.9 
U1  - 519.2 23
PY  - 2011///
CY  - Berlin, Heidelberg
PB  - Springer Berlin Heidelberg
KW  - Mathematics
KW  - Potential theory (Mathematics)
KW  - Distribution (Probability theory)
KW  - Probability Theory and Stochastic Processes
KW  - Potential Theory
N1  - 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
N2  - 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
UR  - http://dx.doi.org/10.1007/978-3-642-21216-1
ER  -