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Random walk systems on graphs

Grant number: 18/16184-7
Support type:Scholarships in Brazil - Scientific Initiation
Effective date (Start): December 01, 2018
Effective date (End): November 30, 2019
Field of knowledge:Physical Sciences and Mathematics - Probability and Statistics
Principal Investigator:Fabio Prates Machado
Grantee:Vitor Hugo Vieira de Lima
Home Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
Associated research grant:17/10555-0 - Stochastic modeling of interacting systems, AP.TEM

Abstract

We intend to continue the research on the particle systems on graphs known as frog model, which was formulated to model the propagation of information or epidemics in a network. In the study of these systems on finite graphs, the main interest is the duration of the process and the proportion of the population informed or infected by the disease after all viruses die. We are interested in working (in a rigorously and through simulations) with versions of the model in a series of graphs (finite, such as bipartite graphs, hypercube or complete graphs or infinite such as $\bbZ^d$) in which the lifetimes of the active particles (spreaders or virus) may not be Markovian.