Universality of the contact process with random dilution

Generalized contact process on random environments.

Spreading from a seed is studied by Monte Carlo simulation on a square lattice with two types of sites affecting the rates of birth and death. These systems exhibit a critical transition between survival and extinction. For time-dependent background, this transition is equivalent to those found in homogeneous systems (i.e., to directed percolation). For frozen backgrounds, the appearance of the...

Asymptotic shape for the contact process in random environment

Large deviations for the contact process in random environment

The asymptotic shape theorem for the contact process in random environment gives the existence of a norm μ on R such that the hitting time t(x) is asymptotically equivalent to μ(x) when the contact process survives. We provide here exponential upper bounds for the probability of the event { t(x) μ(x) 6∈ [1 − ε, 1 + ε]}; these bounds are optimal for independent random environment. As a special c...

The Contact Process in a Dynamic Random Environment By

We study a contact process running in a random environment in Zd where sites flip, independently of each other, between blocking and nonblocking states, and the contact process is restricted to live in the space given by nonblocked sites. We give a partial description of the phase diagram of the process, showing in particular that, depending on the flip rates of the environment, survival of the...

The Contact Process in a Dynamic Random Environment

Z d where sites flip, independently of each other, between blocking and nonblocking states, and the contact process is restricted to live in the space given by nonblocked sites. We give a partial description of the phase diagram of the process, showing in particular that, depending on the flip rates of the environment, survival of the contact process may or may not be possible for large values ...