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Percolation and random interlacements

Grant number: 17/16294-4
Support type:Scholarships in Brazil - Post-Doctorate
Effective date (Start): October 01, 2017
Effective date (End): September 30, 2019
Field of knowledge:Physical Sciences and Mathematics - Probability and Statistics
Principal Investigator:Serguei Popov
Grantee:Daniel Ungaretti Borges
Home Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

Our research intends to investigate some contemporary models in Probability Theory and Stochastic Processes, in particular spacial models with correlations that decay slowly with distance including continuum percolation models and random interlacements. In continuum percolation, we consider problems about planar Boolean models with defects that are not euclidean balls, like elipses model and Poisson stick soups, especially the scale-invariant Poisson stick soup studied by Nacu and Werner. Regarding random interlacements, there are many possible lines of work. Besides considering the classical case of dimensions greater or equal to 3, we also want to work with random interlacements in dimensions 1 and 2.