The Gaussian zoo.
Renze, John, Wagon, Stan, Wick, Brian (2001)
Experimental Mathematics
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Renze, John, Wagon, Stan, Wick, Brian (2001)
Experimental Mathematics
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Manfred G. Madritsch (2008)
Acta Arithmetica
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Rovskiĭ, V.A. (2004)
Zapiski Nauchnykh Seminarov POMI
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Elliot H. Lieb (1990)
Inventiones mathematicae
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Nathan Keller, Elchanan Mossel, Arnab Sen (2014)
Annales de l'I.H.P. Probabilités et statistiques
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In a recent paper, we presented a new definition of influences in product spaces of continuous distributions, and showed that analogues of the most fundamental results on discrete influences, such as the KKL theorem, hold for the new definition in Gaussian space. In this paper we prove Gaussian analogues of two of the central applications of influences: Talagrand’s lower bound on the correlation of increasing subsets of the discrete cube, and the Benjamini–Kalai–Schramm (BKS) noise sensitivity...
Waclaw Timoszyk (1974)
Colloquium Mathematicae
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Helversen-Pasotto, A.
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After some remarks about the analogy between the classical gamma-function and Gaussian sums over finite fields a complete, very short explicit proof is given of an identity expressing a certain sum of products of Gaussian sums as a product of Gaussian sums. This identity is an analogue of the classical Barnes’ first lemma for the gamma-function. Four multiplicative characters of a finite field are concerned; the usually necessary restrictions on the triviality of certain products of...
I. Kátai, P. Liardet (2001)
Acta Arithmetica
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Nicolas Privault, Anthony Réveillac (2011)
ESAIM: Probability and Statistics
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Using integration by parts on Gaussian space we construct a Stein Unbiased Risk Estimator (SURE) for the drift of Gaussian processes, based on their local and occupation times. By almost-sure minimization of the SURE risk of shrinkage estimators we derive an estimation and de-noising procedure for an input signal perturbed by a continuous-time Gaussian noise.
M. Talagrand (1993)
Geometric and functional analysis
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Elchanan Mossel, Joe Neeman (2015)
Journal of the European Mathematical Society
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We prove that under the Gaussian measure, half-spaces are uniquely the most noise stable sets. We also prove a quantitative version of uniqueness, showing that a set which is almost optimally noise stable must be close to a half-space. This extends a theorem of Borell, who proved the same result but without uniqueness, and it also answers a question of Ledoux, who asked whether it was possible to prove Borell’s theorem using a direct semigroup argument. Our quantitative uniqueness result...
Slobodanka S. Mitrović (2005)
Matematički Vesnik
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Michel J. G. Weber (2012)
Colloquium Mathematicae
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We give two examples of periodic Gaussian processes, having entropy numbers of exactly the same order but radically different small deviations. Our construction is based on Knopp's classical result yielding existence of continuous nowhere differentiable functions, and more precisely on Loud's functions. We also obtain a general lower bound for small deviations using the majorizing measure method. We show by examples that our bound is sharp. We also apply it to Gaussian independent sequences...