[ABE-L] Seminário de Probabilidade do IM-UFRJ 06/072026

[Maria Eulalia Vares]

Dear colleagues,

Our next seminar will be held on Monday, *July 6,* from *3:30 p.m. to 4:30
p.m.* (Rio de Janeiro local time). The meeting will take place at *room
C116 - Bloco C - CT – Instituto de Matemática – UFRJ*. There will be no
transmission online.

*Speaker:* Alan Bruno do Nascimento (IM-UFRJ)

*Title:* Survival on percolation models with heavy-tailed one-dimensional
reinforcements



*Abstract:* We study a non-homogeneous Bernoulli bond percolation model on
the graph GxZ. The inhomogeneity comes from an enhanced random region R,
formed by a stack of boxes with iid radii around the root/origin axis.
Outside R, edges are open with subcritical probability p for homogeneous
percolation in GxZ, while inside R edges are open with probability q below
1, which may be highly supercritical.

In a previous work with R. Sanchis, the authors gave moment conditions on
the radii distribution ensuring no percolation for any p below the critical
point and 0<q<1. Here, on the other hand, we aim to show that on euclidean
lattices G=Z^d or on regular trees G=T_d, d>1, there exist distributions
growing fast enough and q₀ < 1, depending on the graph, such that the model
percolates with positive probability for q>q₀.

Joint work with Daniel Ungaretti



More complete information about the seminars can be found at:
https://ppge.im.ufrj.br/seminarios-de-probabilidade/


Sincerely,

Giulio Iacobelli and Maria Eulalia Vares
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