Abstract #302355

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JSM 2003 Abstract #302355
Activity Number: 39
Type: Invited
Date/Time: Sunday, August 3, 2003 : 4:00 PM to 5:50 PM
Sponsor: IMS
Abstract - #302355
Title: Oriented Percolation in a Dependent Environment
Author(s): Maria Eulalia Vares*+
Companies: Instituto De Matematica Pura E Aplicada-IMPA/CNPq
Address: Instituto- Estrada Dona Castorina 110, Rio De Janeiro, , , Brazil
Keywords:
Abstract:

I will discuss results of a joint project by Harry Kesten, Vladas Sidoravicius, and myself, where we consider a two-dimensional oriented percolation problem in a random environment. It may be seen as a discrete time growth model; time instants are first declared to be bad or good, independent of each other. Given the configuration of good/bad times, at the good times, the sites are open with large probability (super-critical for two-dimensional oriented site percolation); at the bad times, the sites have a small probability to be open. We ask if the frequency of bad time instants may be taken small enough so that there is a positive probability of percolation to infinity from the origin. We prove the answer to be positive. Several interesting problems, such as percolation of binary sequences (introduced by I. Benjamini and H. Kesten), percolation on randomly stretched lattices (J. Jonasson, E. Mossel and Y. Peres), and compatibility of binary sequences (P. Winkler), can be formulated as percolation in such an environment. I shall discuss the main ideas behind our proof and the relation to these problems.

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