Open Access
November 2012 Random interlacements and the Gaussian free field
Alain-Sol Sznitman
Ann. Probab. 40(6): 2400-2438 (November 2012). DOI: 10.1214/11-AOP683


We consider continuous time random interlacements on ${\mathbb{Z}}^{d}$, $d\ge3$, and characterize the distribution of the corresponding stationary random field of occupation times. When $d=3$, we relate this random field to the two-dimensional Gaussian free field pinned at the origin by looking at scaled differences of occupation times of long rods by random interlacements at appropriately tuned levels. In the main asymptotic regime, a scaling factor appears in the limit, which is independent of the free field, and distributed as the time-marginal of a zero-dimensional Bessel process. For arbitrary $d\ge3$, we also relate the field of occupation times at a level tending to infinity, to the $d$-dimensional Gaussian free field.


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Alain-Sol Sznitman. "Random interlacements and the Gaussian free field." Ann. Probab. 40 (6) 2400 - 2438, November 2012.


Published: November 2012
First available in Project Euclid: 26 October 2012

zbMATH: 1261.60095
MathSciNet: MR3050507
Digital Object Identifier: 10.1214/11-AOP683

Primary: 60F05 , 60J27 , 60K35

Keywords: Gaussian free field , Occupation times , Random interlacements

Rights: Copyright © 2012 Institute of Mathematical Statistics

Vol.40 • No. 6 • November 2012
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