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The main result of this paper is that almost every realization of the sine-process with one particle removed is a uniqueness set for the Paley-Wiener space; with two particles removed, a zero set for the Paley-Wiener space.
The Patterson-Sullivan construction is proved almost surely to recover every harmonic function in a certain Banach space from its values on the zero set of a Gaussian analytic function on the disk. The argument relies on the slow growth of variance f
We show that Sine$_beta$, the bulk limit of the Gaussian $beta$-ensembles is the spectrum of a self-adjoint random differential operator [ fto 2 {R_t^{-1}} left[ begin{array}{cc} 0 &-tfrac{d}{dt} tfrac{d}{dt} &0 end{array} right] f, qquad f:[0,1)to m
We show how the mathematical structure of large-deviation principles matches well with the concept of coarse-graining. For those systems with a large-deviation principle, this may lead to a general approach to coarse-graining through the variational form of the large-deviation functional.
We prove existence and pathwise uniqueness results for four different types of stochastic differential equations (SDEs) perturbed by the past maximum process and/or the local time at zero. Along the first three studies, the coefficients are no longer
We study the generalizations of Jonathan Kings rank-one theorems (Weak-Closure Theorem and rigidity of factors) to the case of rank-one R-actions (flows) and rank-one Z^n-actions. We prove that these results remain valid in the case of rank-one flows