Dyson's Brownian motions, intertwining and interlacing

By Jon Warren. 2005

134 citations recorded by the source corpus.

A reflected Brownian motion in the Gelfand-Tsetlin cone is used to construct Dyson's process of non-colliding Brownian motions. The key step of the construction is to consider two interlaced families of Brownian paths with paths belonging to the second family reflected off paths belonging to the first. Such families of paths are known to arise in the Arratia flow of coalescing Brownian motions. A determinantal formula for the distribution of coalescing Brownian motions is presented.

Subfields: Applied Mathematics, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/6e532a55bd8f79de45d0f2f5e2b1f9a5ecf25e8e

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In Applied Mathematics

In Mathematical Physics

In Statistics and Probability

Citations in the corpus

Systems of Brownian particles with asymmetric collisions (2012, methodology): “In contrast, the particles in the process introduced by Warren in [34] evolve as independent Brownian motions with constant drift and diffusion coëfficients, and collide in a totally asymmetric manner; that is, the collision local time is assigned entirely to one of the two colliding particles.”
HYBRID ATLAS MODELS (2009, methodology): “Recent work by Warren [24] constructs Dyson’s process using Doob’s h−transform and Brownian motion in the Gelfand-Tsetlin cone, as an extension of Dubédat’s work [11] on the relation between reflected Brownian motions on the wedge and a Bessel process of dimension three.”
Directed polymers and the quantum Toda lattice (2009, background): “Proposition 8.2 has a “symmetric” analogue which can be regarded as a geometric version of a result of Dubedat [16] in the case N = 2, and Warren [62] in the general case.”