An isomorphism theorem for random interlacements

2011/11/21 by Alain-Sol Sznitman · 3 citations
Mathematics · #math.PR #msc:60K35 #msc:60J27 #msc:60G15 #msc:60F05

paper · pdf

published as Electron. Commun. Probab., 17, 9, 1-9, 2012 · 11 pages

arxiv created 2011/11/21 · arxiv updated 2012/02/17

Abstract

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.

Cited by

• The sign clusters of the massless Gaussian free field percolate on ℤ^d, d \geqslant 3 (and more)
• On scaling limits and Brownian interlacements
• Level set percolation for random interlacements and the Gaussian free field

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