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

Grant number: 19/19056-2
Support Opportunities:Scholarships in Brazil - Doctorate
Effective date (Start): February 01, 2020
Effective date (End): January 31, 2025
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). Ministério da Educação (Brasil). 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


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)

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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)
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, . (19/19056-2, 17/10555-0, 18/04764-9)
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., . (20/12868-9, 17/10555-0, 19/19056-2)

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