SPMES: Functional CLT for the Erdős–Rényi giant component

Seminário de Probabilidade e Mecânica Estatística
Título: Functional CLT for the Erdős–Rényi giant component
Palestrante: Josué Corujo Rodríguez, Faculté de Sciences et Technologies
of the Université Paris-Est Créteil

Playlist dos videos: https://bit.ly/30ZkHWe

Resumo: We study the fluctuations of the size (that is, the number of
vertices) of the giant component in the Erdős–Rényi random graph
process. The functional CLT in the supercritical case was recently
obtained by Enriquez, Faraud and Lemaire. Our approach is based on an
exploration algorithm called the simultaneous breadth-first walk,
introduced by Limic in 2019, which encodes the dynamics of the evolution
of the sizes of the connected components of random graph processes. We
will also discuss how our method can be adapted to establish a similar
functional CLT in the barely supercritical regime. This is joint work
with Vlada Limic and Sophie Lemaire.

Apoio:
IMPA
Instituto Superior Técnico de Lisboa
UFBA
UFMG
UFRGS
UFRJ
Unicamp
Universidade do Porto
USP

Comitê científico:
Luiz Renato Fontes (USP)
Tertuliano Franco (UFBA)
Nancy Lopes Garcia (Unicamp)
Patrícia Gonçalves (IST, Lisboa)
Marcelo Hilário (UFMG)
Roberto Imbuzeiro (Coordenador, IMPA)
Claudio Landim (Coordenador, IMPA)
Adriana Neumann (UFRGS)
Serguei Popov (UP, Porto)
Glauco Valle (UFRJ)

Redes Sociais do IMPA: https://linktr.ee/impabr

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