1. CMB 2013 (vol 57 pp. 585)
||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