Factorisation des distributions de Cantor
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R. Berthuet (1972)
Annales scientifiques de l'Université de Clermont. Mathématiques
Michael McCrudden (1981)
Mathematische Zeitschrift
Endre Csáki, Miklós Csörgö, Qi-Man Shao (1992)
Annales de l'I.H.P. Probabilités et statistiques
Hara, Keisuke (2004)
Electronic Communications in Probability [electronic only]
Barbato, David (2005)
Electronic Communications in Probability [electronic only]
Piotr Nayar (2014)
Colloquium Mathematicae
We consider Boolean functions defined on the discrete cube equipped with a product probability measure , where and γ = √(α/β). This normalization ensures that the coordinate functions are orthonormal in . We prove that if the spectrum of a Boolean function is concentrated on the first two Fourier levels, then the function is close to a certain function of one variable. Our theorem strengthens the non-symmetric FKN Theorem due to Jendrej, Oleszkiewicz and Wojtaszczyk. Moreover, in the symmetric...
J. Bass (1989)
Annales de l'I.H.P. Probabilités et statistiques
Vomişescu, Romeo (2002)
General Mathematics
Abdennadher, Ali, Neel, Marie-Christine (2007)
Electronic Journal of Differential Equations (EJDE) [electronic only]
Blower, Gordon (2007)
JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]
Abreu, Victor Perez, Sakuma, Noriyoshi (2008)
Electronic Communications in Probability [electronic only]
I. P. van den Berg, F. Koudjeti (1997)
Annales mathématiques Blaise Pascal
Aldéric Joulin, Nicolas Privault (2010)
ESAIM: Probability and Statistics
We present several functional inequalities for finite difference gradients, such as a Cheeger inequality, Poincaré and (modified) logarithmic Sobolev inequalities, associated deviation estimates, and an exponential integrability property. In the particular case of the geometric distribution on we use an integration by parts formula to compute the optimal isoperimetric and Poincaré constants, and to obtain an improvement of our general logarithmic Sobolev inequality. By a...
Aldéric Joulin, Nicolas Privault (2004)
ESAIM: Probability and Statistics
We present several functional inequalities for finite difference gradients, such as a Cheeger inequality, Poincaré and (modified) logarithmic Sobolev inequalities, associated deviation estimates, and an exponential integrability property. In the particular case of the geometric distribution on we use an integration by parts formula to compute the optimal isoperimetric and Poincaré constants, and to obtain an improvement of our general logarithmic Sobolev inequality. By a limiting procedure we...
Cattiaux, Patrick, Gozlan, Nathael, Guillin, Arnaud, Roberto, Cyril (2010)
Electronic Journal of Probability [electronic only]
Miao, Yu, Li, Junfen (2008)
JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]
Antonio Di Crescenzo, Abdolsaeed Toomaj (2017)
Kybernetika
Recently, a new concept of entropy called generalized cumulative entropy of order was introduced and studied in the literature. It is related to the lower record values of a sequence of independent and identically distributed random variables and with the concept of reversed relevation transform. In this paper, we provide some further results for the generalized cumulative entropy such as stochastic orders, bounds and characterization results. Moreover, some characterization results are derived...
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