12,624 research outputs found
Isoperimetry for spherically symmetric log-concave probability measures
We prove an isoperimetric inequality for probability measures on
with density proportional to , where
is the euclidean norm on and is a non-decreasing
convex function. It applies in particular when with
. Under mild assumptions on , the inequality is
dimension-free if is chosen such that the covariance of 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 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
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