Título: Truncation of long-range percolation model with square non-summable interactions

Palestrante: Bernardo Nunes Borges de Lima (Dep. de Matemática - UFMG)
Data: 09/11/2020
Horário: 15:00 -  16:00. (Rio de Janeiro local time)
Local: Transmissão online

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Resumo: We consider some problems related to the truncation question in long-range percolation. It is given probabilities that certain long-range oriented bonds are open; assuming that these probabilities are not summable, we ask if the probability of percolation is positive when we truncate the graph, disallowing bonds of range above a possibly large but finite threshold. This question is still open if the set of vertices is $\Z^2$. We give some conditions in which the answer is affirmative. One of these results generalize the previous result in [Alves, Hilário, de Lima, Valesin, Journ. Stat. Phys. {\bf 122}, 972 (2017)].

Joint work with Alberto M. Campos.