Dissemination processes on graphs

• Grant number: 20/05555-4
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: August 01, 2020
• End date: November 05, 2021
• Field of knowledge: Physical Sciences and Mathematics - Probability and Statistics - Probability
• Principal Investigator: Luiz Renato Gonçalves Fontes
• Grantee: Daniel Ungaretti Borges
• Host 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

This project aims to investigate dissemination processes on graphs. This kind of model tries to replicate the underlying mechanisms in which information ordiseases spread among individuals of a certain group, taking into consideration their relationship network. Our focus will be in two models, the contact process and rumor processes. The contact process was introduced by Harris (1974) and is well-studied, but recently a new version of the model that allows the regeneration times to be renewal processes was introduced by Fontes and co-authors (2019). We are interested in comprehending the effect of the distribution of regeneration times in the survival of the contact process when the spacial dimension of the process is larger than 1, generalizing previous results. Rumor processes also fit well into this context of dissemination. The fireworks model was introduced by Júnior, Machado and Zuluaga (2011) and considers the evolution of a rumor on a graph, starting from a single vertex. Each vertex has its respective random radius; on time zero the original vertex spreads the rumor to every other vertex within its reach and, successively, vertices that know the rumor at time n spread it, according to their respective radii, at timen+1. We want to understand better which radii distributions allow the rumor to spread indefinitely and also investigate the spreading speed and asymptotic shape for certain graphs. (AU)

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

HILARIO, MARCELO; UNGARETTI, DANIEL. A note on the phase transition for independent alignment percolation. BERNOULLI, v. 28, n. 2, p. 16-pg., 2022-05-01. (20/05555-4)

HILARIO, MARCELO; UNGARETTI, DANIEL; VALESIN, DANIEL; VARES, MARIA EULALIA. Results on the contact process with dynamic edges or under renewals. ELECTRONIC JOURNAL OF PROBABILITY, v. 27, p. 31-pg., 2022-01-01. (20/05555-4)

FONTES, LUIZ RENATO; MOUNTFORD, THOMAS S.; UNGARETTI, DANIEL; VARES, MARIA EULALIA. Renewal Contact Processes: Phase transition and survival. Stochastic Processes and their Applications, v. 161, p. 35-pg., 2023-04-06. (20/05555-4, 17/10555-0)