Markov Paths, Loops and Fields École d'Été de Probabilités de Saint-Flour XXXVIII – 2008
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 studi...
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| Format: | eBook |
| Language: | English |
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Berlin, Heidelberg
Springer Berlin Heidelberg
2011, 2011
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| Edition: | 1st ed. 2011 |
| Series: | École d'Été de Probabilités de Saint-Flour
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| Collection: | Springer eBooks 2005- - Collection details see MPG.ReNa |
Table of Contents:
- 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