Artículos de revistas
The number of open paths in an oriented rho-percolation model
Fecha
2008Registro en:
JOURNAL OF STATISTICAL PHYSICS, v.131, n.2, p.357-379, 2008
0022-4715
10.1007/s10955-008-9506-2
Autor
COMETS, Francis
POPOV, Serguei
VACHKOVSKAIA, Marina
Institución
Resumen
We study the asymptotic properties of the number of open paths of length n in an oriented rho-percolation model. We show that this number is e(n alpha(rho)(1+o(1))) as n ->infinity. The exponent alpha is deterministic, it can be expressed in terms of the free energy of a polymer model, and it can be explicitly computed in some range of the parameters. Moreover, in a restricted range of the parameters, we even show that the number of such paths is n(-1/2)We (n alpha(rho))(1+o(1)) for some nondegenerate random variable W. We build on connections with the model of directed polymers in random environment, and we use techniques and results developed in this context.