Strong result for real zeros of random algebraic polynomials.
Uno, T. (2001)
Journal of Applied Mathematics and Stochastic Analysis
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Uno, T. (2001)
Journal of Applied Mathematics and Stochastic Analysis
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Farahmand, K. (1992)
Journal of Applied Mathematics and Stochastic Analysis
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François Germinet (2007-2008)
Séminaire Équations aux dérivées partielles
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In this review, we first recall a recent Bernoulli decomposition of any given non trivial real random variable. While our main motivation is a proof of universal occurence of Anderson localization in continuum random Schrödinger operators, we review other applications like Sperner theory of antichains, anticoncentration bounds of some functions of random variables, as well as singularity of random matrices.
Nadine Guillotin-Plantard, Clémentine Prieur (2010)
ESAIM: Probability and Statistics
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We prove a central limit theorem for linear triangular arrays under weak dependence conditions. Our result is then applied to dependent random variables sampled by a -valued transient random walk. This extends the results obtained by [N. Guillotin-Plantard and D. Schneider, (2003) 477–497]. An application to parametric estimation by random sampling is also provided.
Jan Rosiński, Wojbor A. Woyczyński (1987)
Colloquium Mathematicae
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R. Kaufman (1970)
Studia Mathematica
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Amini, M., Bozorgnia, A. (2000)
Journal of Applied Mathematics and Stochastic Analysis
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Beg, Ismat, Shahzad, Naseer (1995)
Journal of Applied Mathematics and Stochastic Analysis
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Czesław Stępniak (2015)
Discussiones Mathematicae Probability and Statistics
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Correlation coefficient is a well known measure of (linear) dependence between random variables. In his textbook published in 1980 L.T. Kubik introduced an analogue of such measure for random events A and B and studied its basic properties. We reveal that this measure reduces to the usual correlation coefficient between the indicator functions of A and B. In consequence the resuts by Kubik are obtained and strenghted directly. This is essential because the textbook is recommended by...
Rio Emmanuel (1997)
ESAIM: Probability and Statistics
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