Conditional decoupling of random interlacements

Author(s)

Alves, Caio ^[1] ; Popov, Serguei ^[2]

Affiliation

^[1] Univ Leipzig, Math Inst, Augustuspl 10, Leipzig - Germany

^[2] Univ Estadual Campinas, Inst Math Stat & Sci Computat, Dept Stat, UNICAMP, Rua Sergio Buarque Holanda 651, BR-13083859 Campinas, SP - Brazil

• Document type: Journal article
• Source: ALEA-LATIN AMERICAN JOURNAL OF PROBABILITY AND MATHEMATICAL STATISTICS; v. 15, n. 2, p. 1027-1063, 2018.
• Web of Science Citations: 2

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) A(1 )given the (not very ``bad{''}) configuration on a ``distant{''} set A(2) 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. (AU)

• FAPESP's process: 15/18930-0 - Decoupling in correlated percolation models
• Grantee: Caio Teodoro de Magalhães Alves
• Support Opportunities: Scholarships abroad - Research Internship - Post-doctor
• FAPESP's process: 13/24928-2 - Random walks and dependent percolation
• Grantee: Caio Teodoro de Magalhães Alves
• Support Opportunities: Scholarships in Brazil - Post-Doctoral