26 04 im alumniV8
22 11 im fatiado face
22 11 im fatiado twitter
22 11 im fatiado youtube
22 11 im fatiado gmail
22 11 im fatiado brazil
22 11 im fatiado england
22 11 im fatiado spain

Título: Anisotropic bootstrap percolation
Palestrante: Daniel Ricardo B. Tordecilla

Data: 1 de abril de 2019 (segunda-feira)
Horário: 15h30
Local: Sala B106-a (Bloco B - CT), Instituto de Matemática - UFRJ 

Resumo: Bootstrap percolation is a monotone version of the Glauber dynamics of the Ising model of ferromagnetism. In this talk we will consider nisotropic bootstrap models, which are three-dimensional analogues of a family of (two-dimensional) processes studied by Duminil-Copin, van Enter and Hulshof. In these models the underlying graph G has vertex set [L]3, and the neighbourhood of each vertex consists of the ai nearest neighbours in the ei-direction for each i ∈ {1, 2, 3}, where a1 ≤ a2 ≤ a3. Given an initial configuration in {0, 1}V(G), the system evolves in discrete time in the following way: the state of a vertex v changes from 0 to 1 when it has at least r neighbours in state 1. The initial state is usually chosen to be the product of Bernoulli  easures with density p, and the main question is to determine the so-called critical length for percolation Lc(p), for small values of p.

It turns out that Lc(p) is polynomial if r ≤ a3, exponential if a3 < r ≤ a2 + a3, doubly exponential if a2 + a3 <r ≤ a1 + a2 + a3, and infinite if r > a1 + a2 + a3. In this talk we will focus on the case r = a3 + 1, and show how to determine log Lc(p) up to a constant factor. The main new tool, which we call the beams process, allows one to reduce the problem to proving an exponential decay property for a certain two-dimensional model whose behaviour resembles site percolation.

Para mais informações, clique AQUI.