Geodesic
Soft local times and decoupling of random interlacements
Journal of the European Mathematical Society, Tome 17 (2015) no. 10, pp. 2545-2593 Cet article a éte moissonné depuis la source EMS Press

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In this paper we establish a decoupling feature of the random interlacement process Iu⊂Zd at level u, d≥3. Roughly speaking, we show that observations of Iu restricted to two disjoint subsets A1​ and A2​ of Zd are approximately independent, once we add a sprinkling to the process Iu by slightly increasing the parameter u. Our results differ from previous ones in that we allow the mutual distance between the sets A1​ and A2​ to be much smaller than their diameters. We then provide an important application of this decoupling for which such flexibility is crucial. More precisely, we prove that, above a certain critical threshold u∗∗​, the probability of having long paths that avoid Iu is exponentially small, with logarithmic corrections for d=3.
DOI : 10.4171/jems/565
Classification : 60-XX, 82-XX
Keywords: Random interlacements, stochastic domination, soft local time, connectivity decay, smoothening of discrete sets 
@article{JEMS_2015_17_10_a4,
     author = {Serguei Popov and Augusto Teixeira},
     title = {Soft local times and decoupling of random interlacements},
     journal = {Journal of the European Mathematical Society},
     pages = {2545--2593},
     year = {2015},
     volume = {17},
     number = {10},
     doi = {10.4171/jems/565},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/565/}
}
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Serguei Popov; Augusto Teixeira. Soft local times and decoupling of random interlacements. Journal of the European Mathematical Society, Tome 17 (2015) no. 10, pp. 2545-2593. doi: 10.4171/jems/565

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