2,849 research outputs found
Repulsion of an evolving surface on walls with random heights
We consider the motion of a discrete random surface interacting by exclusion
with a random wall. The heights of the wall at the sites of are i.i.d.\
random variables. Fixed the wall configuration, the dynamics is given by the
serial harness process which is not allowed to go below the wall. We study the
effect of the distribution of the wall heights on the repulsion speed.Comment: 8 page
Two-Dimensional Scaling Limits via Marked Nonsimple Loops
We postulate the existence of a natural Poissonian marking of the double
(touching) points of SLE(6) and hence of the related continuum nonsimple loop
process that describes macroscopic cluster boundaries in 2D critical
percolation. We explain how these marked loops should yield continuum versions
of near-critical percolation, dynamical percolation, minimal spanning trees and
related plane filling curves, and invasion percolation. We show that this
yields for some of the continuum objects a conformal covariance property that
generalizes the conformal invariance of critical systems. It is an open problem
to rigorously construct the continuum objects and to prove that they are indeed
the scaling limits of the corresponding lattice objects.Comment: 25 pages, 5 figure
The K-process on a tree as a scaling limit of the GREM-like trap model
We introduce trap models on a finite volume -level tree as a class of
Markov jump processes with state space the leaves of that tree. They serve to
describe the GREM-like trap model of Sasaki and Nemoto. Under suitable
conditions on the parameters of the trap model, we establish its infinite
volume limit, given by what we call a -process in an infinite -level
tree. From this we deduce that the -process also is the scaling limit of the
GREM-like trap model on extreme time scales under a fine tuning assumption on
the volumes.Comment: Published in at http://dx.doi.org/10.1214/13-AAP937 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Scaling limit for a drainage network model
We consider the two dimensional version of a drainage network model
introduced by Gangopadhyay, Roy and Sarkar, and show that the appropriately
rescaled family of its paths converges in distribution to the Brownian web. We
do so by verifying the convergence criteria proposed by Fontes, Isopi, Newman
and Ravishankar.Comment: 15 page
Two-dimensional Poisson Trees converge to the Brownian web
The Brownian web can be roughly described as a family of coalescing
one-dimensional Brownian motions starting at all times in and at all
points of . It was introduced by Arratia; a variant was then studied by
Toth and Werner; another variant was analyzed recently by Fontes, Isopi, Newman
and Ravishankar. The two-dimensional \emph{Poisson tree} is a family of
continuous time one-dimensional random walks with uniform jumps in a bounded
interval. The walks start at the space-time points of a homogeneous Poisson
process in and are in fact constructed as a function of the point
process. This tree was introduced by Ferrari, Landim and Thorisson. By
verifying criteria derived by Fontes, Isopi, Newman and Ravishankar, we show
that, when properly rescaled, and under the topology introduced by those
authors, Poisson trees converge weakly to the Brownian web.Comment: 22 pages, 1 figure. This version corrects an error in the previous
proof. The results are the sam
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