4 Littelmann paths and Brownian paths
نویسنده
چکیده
We study some path transformations related to Littelmann path model and their applications to representation theory and Brownian motion in a Weyl chamber.
منابع مشابه
. R T ] 1 1 Ja n 20 05 Littelmann paths and Brownian paths
We study some path transformations related to Pitman’s theorem on Brownian motion and the three dimensional Bessel process. We relate these to Littelmann path model, and give applications to representation theory and to Brownian motion in a Weyl chamber.
متن کاملFrom Pitman’s theorem to crystals
We describe an extension of Pitman’s theorem on Brownian motion and the three dimensional Bessel process to several dimensions. We show how this extension is suggested by considering a random walk on a noncommutative space, and is connected with crystals and Littelmann paths.
متن کاملOn the Connection between Young Walls and Littelmann Paths
In the article [7], we developed the combinatorics of Young walls associated with higher level adjoint crystals for the quantum affine algebra Uq(ŝl2). The irreducible highest weight crystal B(λ) of arbitrary level is realized as the affine crystal consisting of reduced Young walls on λ. Littelmann [20] gave a concrete path model with which Joseph and Kashiwara proved that there exists an isomo...
متن کاملTriple Points of Brownian Paths in 3-space
In (3), some of us proved that Brownian paths in n-space have double points with probability 1 if rz = 2 or 3; but, for n > 4, there are no double points with probability 1. The question naturally arises as to whether or not Brownian paths in m-space (n = 2 or 3) have triple points. The case of paths in the plane is settled by (a), where it is shown that, with probability 1, Brownian paths in t...
متن کاملGibbs Measures on Brownian Paths
This is a summary of results based upon 1, 4] outlining how Gibbs measures can be deened on Brownian paths and what are their most important properties. Such Gibbs measures have a number of applications in Euclidean quantum eld theory, statistical mechanics, stochastic (partial) diierential equations and other areas.
متن کامل