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Interpolating Thin-Shell and Sharp Large-Deviation Estimates For Isotropic Log-Concave Measures
Interpolating Thin-Shell Sharp Large-Deviation Estimates Isotropic Log-Concave Measures
2010/11/9
Given an isotropic random vector $X$ with log-concave density in Euclidean space $\Real^n$, we study the concentration properties of $|X|$. We show in particular that: \[ \P(|X| \geq (1+t) \sqrt{n}) ...
Isospectral measures
Isospectral measures math
2010/11/11
In recent papers a number of authors have considered Borel probability measures $\mu$ in $\br^d$ such that the Hilbert space $L^2(\mu)$ has a Fourier basis (orthogonal) of complex exponentials. If $\m...
Pfaffian L-ensembles related to the z-measures on partitions with the Jack parameters 1/2 or 2
the z-measures on partitions the Jack parameters
2010/11/15
We construct Pfaffian L-ensembles related to the z-measures on partitions and to the Plancherel measures on partitions with the Jack parameters 1/2 or 2. The results imply that these measures on part...
Existence of doubling measures via generalised nested cubes
doubling measures via generalised nested cubes
2010/11/9
Using generalised dyadic cubes and the mass distribution principle, we give a straightforward new proof for the existence of doubling measures in complete doubling metric spaces.
We construct a family of measures on $\bbR$ that are purely singular with respect to Lebesgue measure, and yet exhibit universal sine-kernel asymptotics in the bulk. The measures are best described v...
On the finite-dimensional marginals of shift-invariant measures
On the finite-dimensional marginals shift-invariant measures
2010/11/17
Let $\Sigma$ be a finite alphabet, $\Omega=\Sigma^{\mathbb{Z}^{d}}$ equipped with the shift action, and $\mathcal{I}$ the simplex of shift-invariant measures on $\Omega$. We study the relation betwee...