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Limiting Shape for the Contact Process on Random Geometric Graphs

Grant number: 20/12868-9
Support type:Scholarships abroad - Research Internship - Doctorate
Effective date (Start): May 01, 2021
Effective date (End): April 30, 2022
Field of knowledge:Physical Sciences and Mathematics - Probability and Statistics - Probability
Principal Investigator:Cristian Favio Coletti
Grantee:Lucas Roberto de Lima
Supervisor abroad: Daniel Rodrigues Valesin
Home Institution: Centro de Matemática, Computação e Cognição (CMCC). Universidade Federal do ABC (UFABC). Ministério da Educação (Brasil). Santo André , SP, Brazil
Research place: University of Groningen, Netherlands  
Associated to the scholarship:19/19056-2 - Shape theorem for the contact process in random environment on groups with polynomial growth, BP.DR


The contact process on a graph is a model for the spread of an infection where the vertices can alternate between the infected (or occupied) and healthy (or vacant) states. We consider the process defined on the infinite connected component of a random geometric graph in the d-dimensional Euclidean space. A healthy vertex becomes infected at a rate proportional to the number of infected neighboring vertices. An infected vertex becomes healthy at a constant rate. We will study if the random set of sites that were already infected converges almost surely to a deterministic shape. We are also interested in finding related results, such as to specify the limiting shape and possible applications.