Brownian Paths and Cones

4 Littelmann paths and Brownian paths

We study some path transformations related to Littelmann path model and their applications to representation theory and Brownian motion in a Weyl chamber.

Intersection properties of Brownian paths

This review presents a modern approach to intersections of Brownian paths. It exploits the fundamental link between intersection properties and percolation processes on trees. More precisely, a Brownians path is intersect-equivalent to certain fractal percolation. It means that the intersection probabilities of Brownian paths can be estimated up to constant factors by survival probabilities of ...

Cut Points on Brownian Paths

Let X be a standard 2-dimensional Brownian motion. There exists a.s. t ∈ (0, 1) such that X([0, t)) ∩ X((t, 1]) = ∅. It follows that X([0, 1]) is not homeomorphic to the Sierpiński carpet a.s.

Gibbs 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.

Branching Properties of Brownian Paths and Trees