Markov Paths, Loops and Fields

Beschreibung

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.
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. Includes supplementary material: sn.pub/extras

Autor*in

Yves Le Jan

Themen in »Markov Paths, Loops and Fields«

60J27, 60K35 60J45 Free field Markov loops Random Spanning trees

Stimmen zu »Markov Paths, Loops and Fields«

Details

Link teilen