Isoperimetry for spherically symmetric log-concave probability measures

We prove an isoperimetric inequality for probability measures $\mu$ on $\mathbb{R}^n$ with density proportional to $\exp(-\phi(\lambda | x|))$, where $|x|$ is the euclidean norm on $\mathbb{R}^n$ and $\phi$ is a non-decreasing convex function. It applies in particular when $\phi(x)=x^\alpha$ with $\alpha\ge1$. Under mild assumptions on $\phi$, the inequality is dimension-free if $\lambda$ is chosen such that the covariance of $\mu$ is the identity

Aspects of the Electroweak Phase Transition

Presented at the 1992 Meeting of the DPF, Fermilab. The electroweak phase transition is reviewed in light of some recent developments. Emphasis is on the issue whether the transition is first or second order and its possible role in the generation of the baryon asymmetry of the universe.Comment: 5 page

Testing k-monotonicity of a discrete distribution. Application to the estimation of the number of classes in a population

We develop here several goodness-of-fit tests for testing the k-monotonicity of a discrete density, based on the empirical distribution of the observations. Our tests are non-parametric, easy to implement and are proved to be asymptotically of the desired level and consistent. We propose an estimator of the degree of k-monotonicity of the distribution based on the non-parametric goodness-of-fit tests. We apply our work to the estimation of the total number of classes in a population. A large simulation study allows to assess the performances of our procedures.Comment: 32 pages, 8 figure

On Gaussian Brunn-Minkowski inequalities

In this paper, we are interested in Gaussian versions of the classical Brunn-Minkowski inequality. We prove in a streamlined way a semigroup version of the Ehrard inequality for $m$ Borel or convex sets based on a previous work by Borell. Our method also allows us to have semigroup proofs of the geometric Brascamp-Lieb inequality and of the reverse one which follow exactly the same lines