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Branching processes in the phase transition of the Erdos-Renyi random graph

Grant number: 16/10210-0
Support Opportunities:Scholarships in Brazil - Scientific Initiation
Effective date (Start): August 01, 2016
Effective date (End): July 31, 2017
Field of knowledge:Physical Sciences and Mathematics - Probability and Statistics - Probability
Principal Investigator:Pablo Martin Rodriguez
Grantee:Caio Moura Quina
Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
Associated research grant:13/07375-0 - CeMEAI - Center for Mathematical Sciences Applied to Industry, AP.CEPID


Our aim in this project is to study how basic results about the survival probability of branching processes can be applied to obtain result about the emergenceof the giant component in the Erdös-Rényi random graph G(n,p), taking as a basis a recent work by Bollobás and Riordan (2012). The G(n,p) model is the random graph with n vertices, in which each edge is present independently with probability p. This project will allow the student to learn about branching processes, random graphs, and coupling between stochastic processes. The student will prove in detail some results from the literature. In addition, if possible, he will apply the studied topics to understand the behavior of an epidemic propagation on a graph.

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