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Stochastic chains with unbounded memory and random walks on graphs

Grant number: 19/23439-4
Support type:Regular Research Grants
Duration: February 01, 2020 - January 31, 2022
Field of knowledge:Physical Sciences and Mathematics - Probability and Statistics - Probability
Principal Investigator:Alexsandro Giacomo Grimbert Gallo
Grantee:Alexsandro Giacomo Grimbert Gallo
Home Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil

Abstract

The project splits essentially into the study of two random objects. 1- Concerning stochastic chains with unbounded memory, we will continue the researches initiated since my PhD, increasing some new topics of interest. In a generic way, we want to obtain global characterisations of the measures (stationary or not), starting from the knowledge of local rules of interaction. We will focus on concentration inequalities and recurrence theory. 2- Concerning random walks on graphs, we will study the phase transition recurrence/transience in the frog models with random life time, on non-regular or even random trees. Another important question will be to study some properties of the visited sub-tree. This project is about discrete mathematics, it involves several areas related to probability theory (percolation, ergodic theory, statistical physics, statistical inference...). (AU)