Random interlacements and the Soft Local Times technique

• Grant number: 13/00855-6
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: March 01, 2013
• End date: December 31, 2013
• Field of knowledge: Physical Sciences and Mathematics - Probability and Statistics - Probability
• Principal Investigator: Serguei Popov
• Grantee: Darcy Gabriel Augusto de Camargo Cunha
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Associated research grant: 09/52379-8 - Stochastic modeling of interacting systems, AP.TEM

Abstract

The random interlacements process was first presented by Alain-Sol Sznitman in an article of the Annals of Mathematics in 2010. In a heuristic way, we can say that the process describes the behavior of a random Z^d subset formed by random walk trajectories generated in Z^d in a stationary way. This work focus its in the study of the articles developed in the recent years, mainly focusing in the new technique developed by Serguei Popov and Augusto Teixeira called Soft Local Times. By using such technique, we intent to develop new theorems about the random interlacements process and the percolation proprieties of this subset. (AU)