Palestra: Critical scaling for an anisotropic percolation model on Z²
Palestrante: Maria Eulalia Vares (IM-UFRJ)

Data: 27 de maio de 2019 (segunda-feira)
Hora: 15h40
Local: Sala B106-a (Bloco B - CT), Instituto de Matemática - UFRJ

Resumo: We consider an anisotropic finite-range bond percolation model on Z² . On each horizontal layer H_i = {(x, i): x ∈ Z} we have edges h(x, i),(y, i)i for 1 ≤ |x − y| ≤ N. There are also vertical edges connecting two nearest neighbor vertices on distinct lines h(x, i),(x, i + 1)i for x, i ∈ Z. On this graph we consider the following anisotropic independent percolation model: horizontal edges are open with probability 1/(2N), while vertical edges are open with probability ∈ to be suitably tuned as N grows to infinity. The main result tells that if ∈ = κN^− 2/5, then we see a phase transition in κ: there exist positive and finite constants C¹ , C² so that there is no percolation if κ < C¹ while percolation occurs for κ > C² .