Markov loops and renormalization

DOI10.1214/09-AOP509zbMath1197.60075arXiv0802.2478OpenAlexW2016458426MaRDI QIDQ984451

Yves Le Jan

Publication date: 19 July 2010

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0802.2478

zbMATH Keywords

loop ensemblesoccupation fieldfree field

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Probabilistic potential theory (60J45) Continuous-time Markov processes on discrete state spaces (60J27)

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Cites Work

• Contour lines of the two-dimensional discrete Gaussian free field
• A generalization of permanents and determinants
• On the Fock space representation of functionals of the occupation field and their renormalization
• A self-avoiding random walk
• Sample path properties of the local times of strongly symmetric Markov processes via Gaussian processes
• Dirichlet forms and symmetric Markov processes
• The Brownian loop soup
• Conformal invariance of planar loop-erased random walks and uniform spanning trees.
• A characterization of the infinitely divisible squared Gaussian processes
• SLE and the free field: Partition functions and couplings
• Random walk loop soup
• Circulation for recurrent markov chains
• Mesures associées à une forme de Dirichlet. Applications
• The conformally invariant measure on self-avoiding loops
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