Banca de DEFESA: LUCAS ROBERTO DE LIMA

Uma banca de DEFESA de DOUTORADO foi cadastrada pelo programa.
DISCENTE : LUCAS ROBERTO DE LIMA
DATA : 16/08/2024
HORA: 16:15
LOCAL: Auditório 801 no 8º andar do Bloco B da Universidade Federal do ABC
TÍTULO:

Asymptotic Shape of Subadditive Processes on Groups and on Random Geometric Graphs

PÁGINAS: 190
RESUMO:

This doctoral thesis undertakes an in-depth exploration of limiting shape theorems across
diverse mathematical structures, with a specific focus on subadditive processes within
finitelygeneratedgroupsexhibitingpolynomialgrowthrates,aswellasstandard
First-Passage Percolation (FPP) models applied to Random Geometric Graphs (RGGs).
Employing a diverse range of techniques, including subadditive ergodic theorems and
tailored modifications suited for polygonal paths within groups, the thesis examines the
asymptotic shape under varying conditions.The investigation extends to subadditive
cocycles characterized by at least and at most linear growth. Moreover, the study delves
into moderate deviations for FPP models on RGGs, refining previous results with theorems
that quantify its speed of convergence to the limiting shape, the fluctuation of the
geodesics, and its spanning trees.Additionally, we apply the obtained results in a
competition model to verify the positive probability of coexistence of two species
competing for territory in a random geometric graph.

MEMBROS DA BANCA:
Presidente - Interno ao Programa - 1604159 - CRISTIAN FAVIO COLETTI
Membro Titular - Examinador(a) Interno ao Programa - 2278843 - LUIS ENRIQUE RAMIREZ
Membro Titular - Examinador(a) Externo à Instituição - INES ARMENDARIZ
Membro Titular - Examinador(a) Externo à Instituição - LUIZ RENATO GONÇALVES FONTES
Membro Titular - Examinador(a) Externo à Instituição - CHRISTOPHE FREDERIC GALLESCO
Membro Suplente - Examinador(a) Externo ao Programa - 1544346 - JEFERSON CASSIANO
Membro Suplente - Examinador(a) Externo à Instituição - ALEXSANDRO GIACOMO GRIMBERT GALLO
Membro Suplente - Examinador(a) Externo à Instituição - GLAUCO VALLE DA SILVA COELHO