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Jon Warren

Publications and source records attributed to Jon Warren.

24 records · Page 2Linked to original sources
arXiv2007

Dynamics for the Brownian web and the erosion flow

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 Brownian webs are studied, where the second web is obtained from the first by perturbing according to these dynamics. A stochastic flow of kernels, which we call the erosion flow, is obtained via a filtering construction from such coupled Brownian webs, and the N-point motions of this flow of kernels are identified.

math.PR↗
arXiv2005

Dyson's Brownian motions, intertwining and interlacing

A family of reflected Brownian motions is used to construct Dyson's process of non-colliding Brownian motions. A number of explicit formulae are given, including one for the distribution of a family of coalescing Brownian motions.

math.PR↗
arXiv2005

Random orderings of the integers and card shuffling

In this paper we study random orderings of the integers with a certain invariance property. We describe all such orders in a simple way. We define and represent random shuffles of a countable set of labels and then give an interpretation of these orders in terms of a class of generalized riffle shuffles.

math.PR↗
arXiv2005

Dynamics and Endogeny for recursive processes on trees

We consider stochastic processes indexed by the vertices of an infinite binary tree having a simple recursive structure. The value at any vertex is some fixed function of the values at the two daughter vertices together with some independent innovation. Endogeny means the innovations are generating. When endogeny does not hold there exist dynamics in which the innovations are held fixed while some additional randomness on the boundary of the tree is perturbed.

math.PR↗
arXiv2004

A stochastic flow arising in the study of local times

A stochastic flow of homeomorphisms of the real line previously studied by Bass and Burdzy is shown to arise in describing a Brownian motion conditional on knowing its local times on hitting a fixed level. This makes it possible to connect Ray-Knight type results for the flow with the classical Ray-Knight theorems for Brownian motion.

math.PR↗