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Creators/Authors contains: "Bobkov, S G"

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  1. (, Journal of Mathematical Sciences)
    We discuss several uniform bounds on the remainder term in the Fourier inversion formula for increments of distribution functions. These bounds are illustrated by some discrete examples related to the binomial distribution. 
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  2. ; ; (, Electronic Journal of Probability)
    We explore probability distributions on the real line whose Laplace transform admits an upper bound of subgaussian type known as strict subgaussianity. One class in this family corresponds to entire characteristic functions having only real zeros in the complex plane. Using Hadamard’s factorization theorem, we extend this class and propose new sufficient conditions for strict subgaussianity in terms of location of zeros of the associated characteristic functions. The second part of this note deals with Laplace transforms of strictly subgaussian distributions with periodic components. This class contains interesting examples, for which the central limit theorem with respect to the Rényi entropy divergence of infinite order holds. 
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  3. (, Electronic journal of probability)
    Upper bounds are considered for the Fisher information of random vectors in terms of total variation and norms in Sobolev spaces. We also survey and refine a number of known results in this direction. 
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  4. ; (, Theory of probability and its applications)
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  5. ; ; (, Combinatorics probability and computing)
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  6. ; (, The annals of applied probability)
    We present a short and elementary proof of the Ajtai-Koml\'os-Tusn\'ady (AKT) optimal matching theorem in dimension 2 via Fourier analysis and a smoothing argument. The upper bound applies to more general families of samples, including dependent variables, of interest in the study of rates of convergence for empirical measures. Following the recent pde approach by L. Ambrosio, F. Stra and D. Trevisan, we also adapt a simple proof of the lower bound. 
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  7. ; ; (, Springer proceedings in mathematics)
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  8. ; ; (, Springer proceedings in mathematics)
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  9. (, Lecture notes in mathematics)
    B. Klartag, E. Milman (Ed.)
    We consider rates of approximation of distributions of weighted sums of independent, identically distributed random variables by the Edgeworth correction of the 4-th order. 
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  10. ; (, International mathematics research notices)
    null (Ed.)
    We explore an asymptotic behavior of entropies for sums of independent random variables that are convolved with a small continuous noise. 
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