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An isomorphism theorem for random interlacements. (English) Zbl 1247.60135
Summary: 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 \(u\).

MSC:
60K35 Interacting random processes; statistical mechanics type models; percolation theory
60J27 Continuous-time Markov processes on discrete state spaces
60G15 Gaussian processes
60F05 Central limit and other weak theorems
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