Planar aggregation and the coalescing Brownian flow
نویسنده
چکیده
We study a scaling limit associated to a model of planar aggregation. The model is obtained by composing certain independent random conformal maps. The evolution of harmonic measure on the boundary of the cluster is shown to converge to the coalescing Brownian flow.
منابع مشابه
N ov 2 01 1 Hastings – Levitov Aggregation in the Small - Particle Limit
We establish some scaling limits for a model of planar aggregation. The model is described by the composition of a sequence of independent and identically distributed random conformal maps, each corresponding to the addition of one particle. We study the limit of small particle size and rapid aggregation. The process of growing clusters converges, in the sense of Carathéodory, to an inflating d...
متن کاملA superprocess involving both branching and coalescing
Abstract We consider a superprocess with coalescing Brownian spatial motion. We first prove a dual relationship between two systems of coalescing Brownian motions. In consequence we can express the Laplace functionals for the superprocess in terms of coalescing Brownian motions, which allows us to obtain some explicit results. We also point out several connections between such a superprocess an...
متن کاملBalls–in–boxes Duality for Coalescing Random Walks and Coalescing Brownian Motions
We present a duality relation between two systems of coalescing random walks and an analogous duality relation between two systems of coalescing Brownian motions. Our results extends previous work in the literature and we apply it to the study of a system of coalescing Brownian motions with Poisson immigration.
متن کاملSticky Flows on the Circle
The purpose of this note is to give an example of stochastic flows of kernels as defined in [3], which naturally interpolates between the Arratia coalescing flow associated with systems of coalescing independent Brownian particles on the circle and the deterministic diffusion flow (actually, the results are given in the slightly more general framework of symmetric Levy processes for which point...
متن کاملDynamics for the Brownian Web and the Erosion Flow
Abstract. The Brownian web is a random object that occurs as the scaling limit of an infinite system of coalescing random walks. Perturbing this system of random walks by, independently at each point in space-time, resampling the random walk increments, leads to some natural dynamics. In this paper we consider the corresponding dynamics for the Brownian web. In particular, pairs of coupled Brow...
متن کامل