Percolation and random interlacements

• Grant number: 17/16294-4
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: October 01, 2017
• End date: September 30, 2019
• Field of knowledge: Physical Sciences and Mathematics - Probability and Statistics - Probability
• Principal Investigator: Serguei Popov
• Grantee: Daniel Ungaretti Borges
• Host 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.

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

POPOV, SERGUEI; ROLLA, LEONARDO T.; UNGARETTI, DANIEL. Transience of conditioned walks on the plane: encounters and speed of escape. ELECTRONIC JOURNAL OF PROBABILITY, v. 25, 2020. (17/16294-4)