Some results for the quadratic analysis of Gaussian processes and applications
J. Soler (1980)
Banach Center Publications
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J. Soler (1980)
Banach Center Publications
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Piotr Śniady (2006)
Banach Center Publications
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We find the limit distributions for a spectrum of a system of n particles governed by a k-body interaction. The hamiltonian of this system is modelled by a Gaussian random matrix. We show that the limit distribution is a q-deformed Gaussian distribution with the deformation parameter q depending on the fraction k/√n. The family of q-deformed Gaussian distributions include the Gaussian distribution and the semicircular law; therefore our result is a generalization of the results of Wigner...
Oldřich Kropáč (1982)
Aplikace matematiky
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In the paper the basic analytical properties of the MacDonald function (the modified Bessel function of the second kind) are summarized and the properties of some subclasses of distribution functions based on MacDonald function, especially of the types and are discussed. The distribution functions mentioned are useful for analytical modelling of composed (mixed) distributions, especially for products of random variables having distributions of the exponential type. Extensive and...
G. Feldman (1982)
Studia Mathematica
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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...
Peccati, Giovanni (2007)
Electronic Communications in Probability [electronic only]
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Kwapien, S., Pycia, M., Schachermayer, W. (1996)
Electronic Communications in Probability [electronic only]
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Dinh, Khoan T., Nguyen, Nhu T., Nguyen, Truc T. (2003)
International Journal of Mathematics and Mathematical Sciences
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Leonenko, N.N., Anh, V.V. (2001)
Journal of Applied Mathematics and Stochastic Analysis
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Li, Wenbo V. (1999)
Electronic Communications in Probability [electronic only]
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