Asymptotic shape for subadditive processes on groups and on random geometric graphs

• Grant number: 19/19056-2
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: February 01, 2020
• End date: August 31, 2024
• Field of knowledge: Physical Sciences and Mathematics - Probability and Statistics - Probability
• Principal Investigator: Cristian Favio Coletti
• Grantee: Lucas Roberto de Lima
• Host Institution: Centro de Matemática, Computação e Cognição (CMCC). Universidade Federal do ABC (UFABC). Santo André , SP, Brazil
• Associated research grant: 17/10555-0 - Stochastic modeling of interacting systems, AP.TEM
• Associated scholarship(s): 20/12868-9 - Limiting shape for the contact process on random geometric graphs, BE.EP.DR

Abstract

Subadditive processes describe a wide class of random growth models, with the first-passage percolation (FPP) being a significant example. Asymptotic Shape Theorems often relies on the application of subadditive ergodic theorems in conjunction with a group action that preserves the measure. With this motivation, in this work, we explore a generalization of this approach, where the underlying structure is determined by discrete nilpotent groups, in addition to the commonly employed Z^d hypercubic lattice. Furthermore, we investigate the Asymptotic Shape Theorem and its convergence rate in the context of FPP in random environments in R^d, defined on the infinite connected component of a random geometric graph. (AU)

Scientific publications

(The scientific publications listed on this page originate from the Web of Science or SciELO databases. Their authors have cited FAPESP grant or fellowship project numbers awarded to Principal Investigators or Fellowship Recipients, whether or not they are among the authors. This information is collected automatically and retrieved directly from those bibliometric databases.)

COLETTI, CRISTIAN F.; DE LIMA, LUCAS R.; HINSEN, ALEXANDER; JAHNEL, BENEDIKT; VALESIN, DANIEL. Limiting shape for first-passage percolation models on random geometric graphs. JOURNAL OF APPLIED PROBABILITY, v. N/A, p. 19-pg., 2023-04-24. (20/12868-9, 17/10555-0, 19/19056-2)

COLETTI, CRISTIAN F.; DE LIMA, LUCAS R.; GAVA, RENATO J.; LUIZ, DENIS A.. Limit theorems for a random walk with memory perturbed by a dynamical system. Journal of Mathematical Physics, v. 61, n. 10, OCT 1 2020. (19/19056-2, 17/10555-0, 18/04764-9)

DE LIMA, LUCAS R.; VALESIN, DANIEL. Speed of convergence and moderate deviations of FPP on random geometric graphs☆. Stochastic Processes and their Applications, v. 187, p. 23-pg., 2025-04-24. (19/19056-2, 24/06021-4, 20/12868-9)