| 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 |
Abstract 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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