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Cluster continuous time random walks

Agnieszka Jurlewicz, Mark M. Meerschaert, Hans-Peter Scheffler (2011)

Studia Mathematica

In a continuous time random walk (CTRW), a random waiting time precedes each random jump. The CTRW model is useful in physics, to model diffusing particles. Its scaling limit is a time-changed process, whose densities solve an anomalous diffusion equation. This paper develops limit theory and governing equations for cluster CTRW, in which a random number of jumps cluster together into a single jump. The clustering introduces a dependence between the waiting times and jumps that significantly affects...

Clusters in middle-phase percolation on hyperbolic plane

Jan Czajkowski (2011)

Banach Center Publications

I consider p-Bernoulli bond percolation on transitive, nonamenable, planar graphs with one end and on their duals. It is known from [BS01] that in such a graph G we have three essential phases of percolation, i.e. 0 < p c ( G ) < p u ( G ) < 1 , where p c is the critical probability and p u -the unification probability. I prove that in the middle phase a.s. all the ends of all the infinite clusters have one-point boundaries in ∂ℍ². This result is similar to some results in [Lal].

Coexistence probability in the last passage percolation model is 6 - 8 log 2

David Coupier, Philippe Heinrich (2012)

Annales de l'I.H.P. Probabilités et statistiques

A competition model on 2 between three clusters and governed by directed last passage percolation is considered. We prove that coexistence, i.e. the three clusters are simultaneously unbounded, occurs with probability 6 - 8 log 2 . When this happens, we also prove that the central cluster almost surely has a positive density on 2 . Our results rely on three couplings, allowing to link the competition interfaces (which represent the borderlines between the clusters) to some particles in the multi-TASEP, and...

Cogrowth and spectral gap of generic groups

Yann Ollivier (2005)

Annales de l’institut Fourier

The cogrowth exponent of a group controls the random walk spectrum. We prove that for a generic group (in the density model) this exponent is arbitrarily close to that of a free group. Moreover, this exponent is stable under random quotients of torsion-free hyperbolic groups.

Currently displaying 1721 – 1740 of 10055