Markovian loop clusters on graphs
type: Item
instance of: scholarly article
title: Markovian loop clusters on graphs
zbMATH Open document ID: 1311.60015
author: Yves Le Jan
author: Sophie Lemaire
published in: Illinois Journal of Mathematics
publication date: 2014-09-05T00:00:00Z
full work available at URL: https://arxiv.org/abs/1211.0300
full work available at URL: https://projecteuclid.org/euclid.ijm/1408453593
review text: In the paper, the loop clusters induced by Markov loop ensembles on graphs are studied. Some general properties of the clusters are stated and some formulae useful to study the semigroup of the coalescent process are established. Properties of the loop clusters induced by a simple random walk killed at a constant rate on different graphs are studied.
Mathematics Subject Classification ID: 60C05
Mathematics Subject Classification ID: 60J10
Mathematics Subject Classification ID: 60G55
Mathematics Subject Classification ID: 60K35
Mathematics Subject Classification ID: 05C40
zbMATH DE Number: 6340288
zbMATH Keywords: graph
zbMATH Keywords: loop
zbMATH Keywords: cluster
zbMATH Keywords: Markovian loop
zbMATH Keywords: Poissonian ensembles
reviewed by: U. A. Rozikov
MaRDI profile type: Publication
arXiv ID: 1211.0300
cites work: Random Walk: A Modern Introduction
cites work: Random walk loop soup
cites work: Markov paths, loops and fields. École d'Été de Probabilités de Saint-Flour XXXVIII -- 2008
cites work: Markovian loop clusters
cites work: Conformal loop ensembles: the Markovian characterization and the loop-soup construction
cites work: SLEs as boundaries of clusters of Brownian loops
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description: scientific article; zbMATH DE number 6340288