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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

An Improved Decoupling Inequality for Random Interlacements

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de Bernardini, Diego F. [1] ; Gallesco, Christophe [1] ; Popov, Serguei [1]
Total Authors: 3
[1] Univ Estadual Campinas, UNICAMP, Inst Math Stat & Sci Computat, Dept Stat, Campinas, SP - Brazil
Total Affiliations: 1
Document type: Journal article
Source: Journal of Statistical Physics; v. 177, n. 6, p. 1216-1239, DEC 2019.
Web of Science Citations: 0

In this paper we obtain a decoupling feature of the random interlacements process I-u subset of Z(d), at level u, d >= 3. More precisely, we show that the trace of the random interlacements process on two disjoint finite sets, F and its translated F + x, can be coupled with high probability of success, when parallel to x parallel to is large, with the trace of a process of independent excursions, which we call the noodle soup process. As a consequence, we obtain an upper bound on the covariance between two {[}0, 1]-valued functions depending on the configuration of the random interlacements on F and F + x, respectively. This improves a previous bound obtained by Sznitman (Ann Math 2(171):2039-2087, 2010). (AU)

FAPESP's process: 17/02022-2 - Random interlacement models
Grantee:Serguei Popov
Support Opportunities: Regular Research Grants
FAPESP's process: 14/14323-9 - On the Dependence Structure in Random Interlacements and the Meeting Time of Random Walks in Random Environments
Grantee:Diego Fernando de Bernardini
Support Opportunities: Scholarships in Brazil - Post-Doctoral
FAPESP's process: 17/10555-0 - Stochastic modeling of interacting systems
Grantee:Fabio Prates Machado
Support Opportunities: Research Projects - Thematic Grants
FAPESP's process: 17/19876-4 - Asymptotic properties of chains of infinite order
Grantee:Christophe Frédéric Gallesco
Support Opportunities: Regular Research Grants