1. CMB Online first
|Short Probabilistic Proof of the Brascamp-Lieb and Barthe Theorems|
We give a short proof of the Brascamp-Lieb theorem, which asserts that a certain general form of Young's convolution inequality is saturated by Gaussian functions. The argument is inspired by Borell's stochastic proof of the PrÃ©kopa-Leindler inequality and applies also to the reversed Brascamp-Lieb inequality, due to Barthe.
Keywords:functional inequalities, Brownian motion
2. CMB 2008 (vol 51 pp. 146)
|Stepping-Stone Model with Circular Brownian Migration |
In this paper we consider the stepping-stone model on a circle with circular Brownian migration. We first point out a connection between Arratia flow on the circle and the marginal distribution of this model. We then give a new representation for the stepping-stone model using Arratia flow and circular coalescing Brownian motion. Such a representation enables us to carry out some explicit computations. In particular, we find the distribution for the first time when there is only one type left across the circle.
Keywords:stepping-stone model, circular coalescing Brownian motion, Arratia flow, duality, entrance law