Conditional decoupling of random interlacements

Caio Alves; Serguei Popov

doi:10.30757/ALEA.v15-38

Conditional decoupling of random interlacements

Caio Alves
, Serguei Popov

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

We prove a conditional decoupling inequality for the model of random interlacements in dimension d ≥ 3: the conditional law of random interlacements on a box (or a ball) A₁ given the (not very "bad") configuration on a "distant" set A₂ does not differ a lot from the unconditional law. The main method we use is a suitable modification of the soft local time method of Popov and Teixeira (2015), that allows dealing with conditional probabilities.

Original language	English
Pages (from-to)	1027-1063
Number of pages	37
Journal	Alea (Rio de Janeiro)
Volume	15
Issue number	2
DOIs	https://doi.org/10.30757/ALEA.v15-38
State	Published - 2018
Externally published	Yes

Funding

Caio Alves was supported by FAPESP (grants 2013/24928-2 and 2013/24928-2). Serguei Popov was supported by CNPq (grant 300886/2008) and FAPESP (grant 2009/523798).

Keywords

Random interlacements
Soft local time
Stochastic domination

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10.30757/ALEA.v15-38

Cite this

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AB - We prove a conditional decoupling inequality for the model of random interlacements in dimension d ≥ 3: the conditional law of random interlacements on a box (or a ball) A1 given the (not very "bad") configuration on a "distant" set A2 does not differ a lot from the unconditional law. The main method we use is a suitable modification of the soft local time method of Popov and Teixeira (2015), that allows dealing with conditional probabilities.

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KW - Soft local time

KW - Stochastic domination

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Conditional decoupling of random interlacements

Abstract

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