### On the correct discrimination of Gaussian hypotheses. II.

Rovskiĭ, V.A. (2004)

Zapiski Nauchnykh Seminarov POMI

Similarity:

Skip to main content (access key 's'),
Skip to navigation (access key 'n'),
Accessibility information (access key '0')

Rovskiĭ, V.A. (2004)

Zapiski Nauchnykh Seminarov POMI

Similarity:

Manfred G. Madritsch (2008)

Acta Arithmetica

Similarity:

Yuichi Futa, Hiroyuki Okazaki, Daichi Mizushima, Yasunari Shidama (2013)

Formalized Mathematics

Similarity:

Gaussian integer is one of basic algebraic integers. In this article we formalize some definitions about Gaussian integers [27]. We also formalize ring (called Gaussian integer ring), Z-module and Z-algebra generated by Gaussian integer mentioned above. Moreover, we formalize some definitions about Gaussian rational numbers and Gaussian rational number field. Then we prove that the Gaussian rational number field and a quotient field of the Gaussian integer ring are isomorphic. ...

Elliot H. Lieb (1990)

Inventiones mathematicae

Similarity:

Nathan Keller, Elchanan Mossel, Arnab Sen (2014)

Annales de l'I.H.P. Probabilités et statistiques

Similarity:

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

Similarity:

M. Talagrand (1993)

Geometric and functional analysis

Similarity:

Nicolas Privault, Anthony Réveillac (2011)

ESAIM: Probability and Statistics

Similarity:

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.

Elchanan Mossel, Joe Neeman (2015)

Journal of the European Mathematical Society

Similarity:

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...

Bakirov, N.K., Székely, G.J. (2005)

Zapiski Nauchnykh Seminarov POMI

Similarity:

Michel J. G. Weber (2012)

Colloquium Mathematicae

Similarity:

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...

F. Barthe, D. Cordero-Erausquin, M. Fradelizi (2001)

Studia Mathematica

Similarity:

We derive the equivalence of different forms of Gaussian type shift inequalities. This completes previous results by Bobkov. Our argument strongly relies on the Gaussian model for which we give a geometric approach in terms of norms of barycentres. Similar inequalities hold in the discrete setting; they improve the known results on the so-called isodiametral problem for the discrete cube. The study of norms of barycentres for subsets of convex bodies completes the exposition. ...

Pathmanabhan, A., Dinesh, S. (2007)

Discrete Dynamics in Nature and Society

Similarity:

Nicolas Privault, Anthony Réveillac (2012)

ESAIM: Probability and Statistics

Similarity:

I. Kátai, P. Liardet (2001)

Acta Arithmetica

Similarity: