Markovian loop clusters on graphs
Résumé
The loop clusters of Poissonian ensembles of Markov loops on a finite or countable graph induce a coalescent process on the vertices of the graph. After a description of some general properties of the coalescent process, we study the loop clusters defined by a simple random walk killed at a constant rate on three different graphs: the integer number line $\mathbb{Z}$, the integer lattice $\mathbb{Z}^d$ with $d\geq 2$ and the complete graph.
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