Markov paths, loops and fields: École D'été de Probabilités de Saint-Flour VIII – 2008
Jan, Yves le
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 fre 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. St Flour Lecture notes+ additional material. A large part of the content is new. There is no really similar book. INDICE: 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 spanningtrees. 9 Reflection positivity. 10 The case of general symmetric Markov processes.
- ISBN: 978-3-642-21215-4
- Editorial: Springer Berlin Heidelberg
- Encuadernacion: Rústica
- Páginas: 134
- Fecha Publicación: 31/07/2011
- Nº Volúmenes: 1
- Idioma: Inglés