84 citations · 508 across the 36 of their papers we have counts for
24 papers · 1 filter
On rate of convergence to the Poisson law of the number of cycles in the generalized random graphs
Sergey G. Bobkov, Maria A. Danshina, Vladimir V. Ulyanov
Convergence of order is obtained for the distance in total variation between the Poisson distribution and the distribution of the number of fixed size cycles in gen…
Two-sided inequalities for the density function's maximum of weighted sum of chi-square variables
Sergey G. Bobkov, Alexey A. Naumov, Vladimir V. Ulyanov
Two--sided bounds are constructed for a probability density function of a weighted sum of chi-square variables. Both cases of central and non-central chi-square variables are consi…
Poincaré Inequalities and Normal Approximation for Weighted Sums
S. G. Bobkov, G. P. Chistyakov, F. Götze
Under Poincaré-type conditions, upper bounds are explored for the Kolmogorov distance between the distributions of weighted sums of dependent summands and the normal law. Based on…
Concentration functions and entropy bounds for discrete log-concave distributions
Sergey G. Bobkov, Arnaud Marsiglietti, James Melbourne
Two-sided bounds are explored for concentration functions and Rényi entropies in the class of discrete log-concave probability distributions. They are used to derive certain varian…
A simple Fourier analytic proof of the AKT optimal matching theorem
Sergey Bobkov, Michel Ledoux
We present a short and elementary proof of the Ajtai-Komlós-Tusnády (AKT) optimal matching theorem in dimension 2 via Fourier analysis and a smoothing argument. The upper bound app…
Non-Uniform Bounds in the Poisson Approximation with Applications to Informational Distances. II
S. G. Bobkov, G. P. Chistyakov, F. Götze
We explore asymptotically optimal bounds for deviations of distributions of independent Bernoulli random variables from the Poisson limit in terms of the Shannon relative entropy a…