| 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). 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 |
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) | |
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