Branching random walk with catalysts.
On long range percolation with heavy tails.
Asymptotic behavior of a stochastic combustion growth process
We study a continuous time growth process on the -dimensional hypercubic lattice , which admits a phenomenological interpretation as the combustion reaction , where represents heat particles and inert particles. This process can be described as an interacting particle system in the following way: at time 0 a simple symmetric continuous time random walk of total jump rate one begins to move from the origin of the hypercubic lattice; then, as soon as any random walk visits a site previously...
Connectivity bounds for the vacant set of random interlacements
The model of random interlacements on ℤ, ≥3, was recently introduced in [Vacant set of random interlacements and percolation. Available at http://www.math.ethz.ch/u/sznitman/preprints]. A non-negative parameter parametrizes the density of random interlacements on ℤ. In the present note we investigate connectivity properties of the vacant set left by random interlacements at level , in the non-percolative regime >∗, with ∗ the non-degenerate critical parameter for the percolation of the vacant...
Limit velocity for a driven particle in a random medium with mass aggregation
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