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Creators/Authors contains: "Bobkov, Sergey"

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  1. ; (, Journal of Functional Analysis)
    The paper is devoted to the investigation of Esscher’s transform on high dimensional Euclidean spaces in the light of its application to the central limit theorem. With this tool, we explore necessary and sufficient conditions of normal approximation for normalized sums of i.i.d. random vectors in terms of the Rényi divergence of infinite order, extending recent one dimensional results. 
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    Free, publicly-accessible full text available September 1, 2026
  2. ; (, Pure and applied functional analysis)
    Covariance representations are developed for the uniform distributions on the Euclidean spheres in terms of spherical gradients and Hessians. They are applied to derive a number of Sobolev type inequalities and to recover and refine the concentration of measure phenomenon, including second order concentration inequalities. A detail account is also given in the case of the circle, with a short overview of Hoeffding’s kernels and covariance identities in the class of periodic functions. 
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    Free, publicly-accessible full text available April 9, 2026
  3. ; (, Lithuanian mathematical journal)
    Berry–Esseen-type bounds are developed in the multidimensional local limit theorem in terms of the Lyapunov coefficients and maxima of involved densities. 
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    Free, publicly-accessible full text available March 20, 2026
  4. ; (, The Annals of Probability)
    For normalized sums Zn of i.i.d. random variables, we explore necessary and sufficient conditions, which guarantee the normal approximation with respect to the Rényi divergence of infinite order. In terms of densities pn of Zn, this is a strengthened variant of the local limit theorem taking the form sup (pn(x)− ϕ(x))/ϕ(x)→0 as n→∞. 
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    Free, publicly-accessible full text available March 1, 2026
  5. ; (, Probability Surveys)
    We give an overview of various results and methods related to information-theoretic distances of Rényi type in the light of their applications to the central limit theorem (CLT). The first part (Sections 1–9) is devoted to the total variation and the Kullback-Leibler distance (relative entropy). In the second part (Sections 10–15) we discuss general properties of Rényi and Tsall is divergences of order alpha > 1, and then in the third part (Sections 16–21) we turn to the CLT and non-uniform local limit theorems with respect to these strong distances. In the fourth part (Sections 22–31), we discuss recent results on strictly subgaussian distributions and describe necessary and sufficient conditions which ensure the validity of the CLT with respect to the Rényi divergence of infinite order. 
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    Free, publicly-accessible full text available January 1, 2026
  6. ; (, Journal of Mathematical Sciences)
    We start with a brief survey on the Hoeffding kernels, its properties, related spectral decompositions, and discuss marginal distributions of Hoeffding measures. In the second part of this note, one dimensional covariance representations are considered over compactly supported probability distributions in the class of periodic smooth functions. Hoeffding’s kernels are used in the construction of mixing measures whose marginals are multiples of given probability distributions, leading to optimal kernels in periodic covariance representations. 
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    Free, publicly-accessible full text available December 1, 2025
  7. ; (, Pure and applied functional analysis)
    Pursuing an earlier paper on the entropic isoperimetric inequalities, we discuss optimal bounds on the Renyi entropies in terms of the Fisher information of order s. 
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    Free, publicly-accessible full text available November 9, 2025
  8. ; (, Electronic Journal of Probability)
    We discuss a natural extension of Gilles Pisier’s approach to the study of measure concentration, isoperimetry, and Poincaré-type inequalities. This approach allows one to explore counterparts of various results about Gaussian measures in the class of rotationally invariant probability distributions on Euclidean spaces, including multidimensional Cauchy measures. 
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    Full Text Available 
  9. (, Journal of Fourier Analysis and Applications)
    We discuss some variants of the Berry–Esseen inequality in terms of Lyapunov coefficients which may provide sharp rates of normal approximation. 
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  10. (, The Annals of Probability)
    Upper pointwise bounds are considered for convolution of bounded densities in terms of the associated Laplace and Legendre transforms. Applications of these bounds are illustrated in the central limit theorem with respect to the Rényi divergence. 
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