Electronic Communications in Probability

An isomorphism theorem for random interlacements

Alain-Sol Sznitman

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We consider continuous-time random interlacements on a transient weighted graph. We prove an identity in law relating the field of occupation times of random interlacements at level u to the Gaussian free field on the weighted graph. This identity is closely linked to the generalized second Ray-Knight theorem, and uniquely determines the law of occupation times of random interlacements at level u.<br /><br />

Article information

Electron. Commun. Probab., Volume 17 (2012), paper no. 9, 9 pp.

Accepted: 11 February 2012
First available in Project Euclid: 7 June 2016

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Zentralblatt MATH identifier

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 60J27: Continuous-time Markov processes on discrete state spaces 60G15: Gaussian processes 60F05: Central limit and other weak theorems

random interlacements Gaussian free field isomorphism theorem generalized second Ray-Knight theorem

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Sznitman, Alain-Sol. An isomorphism theorem for random interlacements. Electron. Commun. Probab. 17 (2012), paper no. 9, 9 pp. doi:10.1214/ECP.v17-1792. https://projecteuclid.org/euclid.ecp/1465263142

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