Random interlacements via Kuznetsov measures

URL:	https://arxiv.org/abs/1501.00649
Additional URL:	https://arxiv.org/pdf/1501.00649.pdf
Document Type:	Working paper
Year of publication:	2014
Place of publication:	Mannheim [u.a.]
Publication language:	English
Institution:	School of Business Informatics and Mathematics > Probability Theory (Döring 2017-)
Subject:	510 Mathematics
Abstract:	The aim of this note is to give an alternative construction of interlacements - as introduced by Sznitman - which makes use of classical probabilistic potential theory. In particular, we outline that the intensity measure of an interlacement is known in probabilistic potential theory under the name "approximate Markov chain" or "quasi-process". We provide a simple construction of random interlacements through (unconditioned) two-sided Brownian motions (resp. two-sided random walks) involving Mitro's general construction of Kuznetsov measures and a Palm measures relation due to Fitzsimmons. In particular, we show that random interlacement is a Poisson cloud (`soup') of two-sided random walks (or Brownian motions) started in Lebesgue measure and restricted on being closest to the origin at time between 0 and 1 - modulus time-shift.