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arXiv · 0709.3039

Random even graphs

Geoffrey Grimmett·Svante Janson
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Abstract

We study a random even subgraph of a finite graph $G$ with a general edge-weight $p\in(0,1)$. We demonstrate how it may be obtained from a certain random-cluster measure on $G$, and we propose a sampling algorithm based on coupling from the past. A random even subgraph of a planar lattice undergoes a phase transition at the parameter-value $\frac 12 \pc$, where $\pc$ is the critical point of the $q=2$ random-cluster model on the dual lattice. The properties of such a graph are discussed, and are related to Schramm--Löwner evolutions (SLE).

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Geoffrey Grimmett, Svante Janson. 2009-03-25. Random even graphs. https://arxiv.org/abs/0709.3039

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