The hierarchical Cannings process in random environment

The Random Average Process and Random Walk in a Space-time Random Environment in One Dimension

We study space-time fluctuations around a characteristic line for a onedimensional interacting system known as the random average process. The state of this system is a real-valued function on the integers. New values of the function are created by averaging previous values with random weights. The fluctuations analyzed occur on the scale n where n is the ratio of macroscopic and microscopic sc...

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 ...

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...