Markovian loop clusters on graphs

zbMath1311.60015arXiv1211.0300MaRDI QIDQ405405

Yves Le Jan, Sophie Lemaire

Publication date: 5 September 2014

Published in: Illinois Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1211.0300

zbMATH Keywords

clustergraphloopMarkovian loopPoissonian ensembles

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Markov chains (discrete-time Markov processes on discrete state spaces) (60J10) Combinatorial probability (60C05) Connectivity (05C40) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55)

Related Items (10)

Phase transition in loop percolation ⋮ Percolation and isoperimetry on roughly transitive graphs ⋮ Percolation of worms ⋮ Supercritical loop percolation on \(\mathbb{Z}^d\) for \(d \geq 3\) ⋮ Equality of critical parameters for percolation of Gaussian free field level sets ⋮ Markov loops, free field and Eulerian networks ⋮ Decoupling inequalities and supercritical percolation for the vacant set of random walk loop soup ⋮ From loop clusters and random interlacements to the free field ⋮ On Markovian random networks ⋮ Markov loops in discrete spaces

Cites Work

• Markovian loop clusters
• Markov paths, loops and fields. École d'Été de Probabilités de Saint-Flour XXXVIII -- 2008
• SLEs as boundaries of clusters of Brownian loops
• Conformal loop ensembles: the Markovian characterization and the loop-soup construction
• Random walk loop soup
• Random Walk: A Modern Introduction

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