04/09/26 - Seminário do Programa Interinstitucional de Pós-Graduação em Estatística (PIPGEs) da UFSCar-USP

Nome: Alan Nascimento (PIPGEs - UFSCar-USP)

Título: Inhomogeneous percolation and random reinforcements

Resumo: First introduced to model the flow of fluids through porous
media in 1957, Bernoulli percolation has become a central subject in
probability theory. In its classical, homogeneous formulation, every
edge of a lattice is independently declared open with probability p
and closed with probability 1-p. If there exists an infinite path of
open edges starting from the origin, we say that the model percolates.
This gives rise to a sharp phase transition at a critical threshold
p=p_c, where percolation occurs strictly above p_c and is absent below
it.

Varying the opening probabilities across different regions of the
graph leads to the study of inhomogeneous models, where one
investigates whether local flow privileges or defects alter the global
phenomena observed in the homogeneous setting. In this talk, we show
some classical and modern results in this direction, considering both
deterministic and random distinguished regions. Finally, we present
recent work investigating percolation on product graphs of the form
GxZ enhanced by random one-dimensional reinforcements along an axis.

Local: Sala 6 do CINA-UFSCar (São Carlos)

Todos são bem-vindos!