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S. G. Bobkov

Publications and source records attributed to S. G. Bobkov.

At least 19 recordsLinked to original sources
arXiv2025

Rényi Divergences in Central Limit Theorems: Old and New

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 Tsallis divergences of order $α>1$, 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.

cs.IT↗
arXiv2023

Asymptotic Expansions and two-sided Bounds in Randomized Central Limit Theorems

Lower and upper bounds are explored for the uniform (Kolmogorov) and $L^2$-distances between the distributions of weighted sums of dependent summands and the normal law. The results are illustrated for several classes of random variables whose joint distributions are supported on Euclidean spheres. We also survey several results on improved rates of normal approximation in randomized central limit theorems.

math.PR↗
arXiv2023

Strictly subgaussian probability distributions

We explore the class of probability distributions on the real line whose Laplace transform admits a strong upper bound of subgaussian type. Using Hadamard's factorization theorem, we extend the class $\mathfrak L$ of Newman and propose new sufficient conditions for this property in terms of location of zeros of the associated characteristic functions in the complex plane. The second part of this note deals with Laplace transforms of strictly subgaussian distributions with periodic components. This subclass contains interesting examples, for which the central limit theorem with respect to the Rényi entropy divergence of infinite order holds.

math.PR↗
arXiv2020

Poincaré Inequalities and Normal Approximation for Weighted Sums

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 improved concentration inequalities on high-dimensional Euclidean spheres, the results extend and refine previous results to non-symmetric models.

math.PR↗
arXiv2019

Normal Approximation for Weighted Sums under a Second Order Correlation Condition

Under correlation-type conditions, we derive an upper bound of order $(\log n)/n$ for the average Kolmogorov distance between the distributions of weighted sums of dependent summands and the normal law. The result is based on improved concentration inequalities on high-dimensional Euclidean spheres. Applications are illustrated on the example of log-concave probability measures.

math.PR↗
arXiv2017

High-energy gamma-ray studying with GAMMA-400

Extraterrestrial gamma-ray astronomy is now a source of new knowledge in the fields of astrophysics, cosmic-ray physics, and the nature of dark matter. The next absolutely necessary step in the development of extraterrestrial high-energy gamma-ray astronomy is the improvement of the physical and technical characteristics of gamma-ray telescopes, especially the angular and energy resolutions. Such a new generation telescope will be GAMMA-400. GAMMA-400, currently developing gamma-ray telescope, together with X-ray telescope will precisely and detailed observe in the energy range of ~20 MeV to ~1000 GeV and 3-30 keV the Galactic plane, especially, Galactic Center, Fermi Bubbles, Crab, Cygnus, etc. The GAMMA- 400 will operate in the highly elliptic orbit continuously for a long time with the unprecedented angular (~0.01° at Eγ = 100 GeV) and energy (~1% at Eγ = 100 GeV) resolutions better than the Fermi-LAT, as well as ground gamma-ray telescopes, by a factor of 5-10. GAMMA-400 will permit to resolve gamma rays from annihilation or decay of dark matter particles, identify many discrete sources (many of which are variable), to clarify the structure of extended sources, to specify the data on the diffuse emission.

astro-ph.IM↗
arXiv2017

The high-performance data acquisition system for the GAMMA-400 satellite-borne gamma-ray telescope

The future GAMMA-400 space mission is aimed for the study of gamma rays in the energy range from ~20 MeV up to ~1 TeV. The observations will carry out with GAMMA-400 gamma-ray telescope installed on-board the Russian Space Observatory. We present the detailed description of the architecture and performances of scientific data acquisition system (SDAQ) developing by SRISA for the GAMMA-400 instrument. SDAQ provides the collection of the data from telescope detector subsystems (up to 100 GB per day), the preliminary processing of scientific information and its accumulation in mass memory, transferring the information from mass memory to the satellite high-speed radio line for its transmission to the ground station, the control and monitoring of the telescope subsystems. SDAQ includes special space qualified chipset designed by SRISA and has scalable modular net structure based on fast and high-reliable serial interfaces.

astro-ph.IM↗
arXiv2016

Improvement of the GAMMA-400 physical scheme for precision gamma-ray emission investigations

The main goal for the GAMMA-400 gamma-ray telescope mission is to perform a sensitive search for signatures of dark matter particles in high-energy gamma-ray emission. Measurements will also concern the following scientific goals: detailed study of the Galactic center region, investigation of point and extended gamma-ray sources, studies of the energy spectra of Galactic and extragalactic diffuse emissions. To perform these measurements the GAMMA-400 gamma-ray telescope possesses unique physical characteristics for energy range from ~20 MeV to ~1000 GeV in comparison with previous and current space and ground-based experiments. The major advantage of the GAMMA-400 instrument is excellent angular and energy resolutions for gamma-rays above 10 GeV. The gamma-ray telescope angular and energy resolutions for the main aperture at 100-GeV gamma rays are ~0.01 deg and ~1%, respectively. The special goal is to improve physical characteristics in the low- energy range from ~20 MeV to 100 MeV. Minimizing the amount of dead matter in the telescope aperture allows us to obtain the angular and energy resolutions better in this range than in current space missions. The gamma-ray telescope angular resolution at 50-MeV gamma rays is better than 5 deg and energy resolution is ~10%. We report the method providing these results.

astro-ph.IM↗
arXiv2016

Rényi divergence and the central limit theorem

We explore properties of the $χ^2$ and more general Rényi (Tsallis) distances to the normal law. In particular we provide necessary and sufficient conditions for the convergence to the normal law in the central limit theorem using these distances. Moreover, we derive exact rates of convergence in these distances with respect to an increasing number of summands.

math.PR↗
arXiv2015

GAMMA-400 gamma-ray observatory

The GAMMA-400 gamma-ray telescope with excellent angular and energy resolutions is designed to search for signatures of dark matter in the fluxes of gamma-ray emission and electrons + positrons. Precision investigations of gamma-ray emission from Galactic Center, Crab, Vela, Cygnus, Geminga, and other regions will be performed, as well as diffuse gamma-ray emission, along with measurements of high-energy electron + positron and nuclei fluxes. Furthermore, it will study gamma-ray bursts and gamma-ray emission from the Sun during periods of solar activity. The energy range of GAMMA-400 is expected to be from ~20 MeV up to TeV energies for gamma rays, up to 20 TeV for electrons + positrons, and up to 10E15 eV for cosmic-ray nuclei. For high-energy gamma rays with energy from 10 to 100 GeV, the GAMMA-400 angular resolution improves from 0.1° to ~0.01° and energy resolution from 3% to ~1%; the proton rejection factor is ~5x10E5. GAMMA-400 will be installed onboard the Russian space observatory.

astro-ph.IM↗
arXiv2015

A separation of electrons and protons in the GAMMA-400 gamma-ray telescope

The GAMMA-400 gamma-ray telescope is intended to measure the fluxes of gamma rays and cosmic-ray electrons and positrons in the energy range from 100 MeV to several TeV. Such measurements concern with the following scientific goals: search for signatures of dark matter, investigation of gamma-ray point and extended sources, studies of the energy spectra of Galactic and extragalactic diffuse emission, studies of gamma-ray bursts and gamma-ray emission from the active Sun, as well as high-precision measurements of spectra of high-energy electrons and positrons, protons, and nuclei up to the knee. The main components of cosmic rays are protons and helium nuclei, whereas the part of lepton component in the total flux is ~10E-3 for high energies. In present paper, the capability of the GAMMA-400 gamma-ray telescope to distinguish electrons and positrons from protons in cosmic rays is investigated. The individual contribution to the proton rejection is studied for each detector system of the GAMMA-400 gamma-ray telescope. Using combined information from all detector systems allow us to provide the proton rejection from electrons with a factor of ~4x10E5 for vertical incident particles and ~3x10E5 for particles with initial inclination of 30 degrees. The calculations were performed for the electron energy range from 50 GeV to 1 TeV.

astro-ph.IM↗
arXiv2015

Study of the Gamma-ray performance of the GAMMA-400 Calorimeter

GAMMA-400 is a new space mission, designed as a dual experiment, capable to study both high energy gamma rays (from $\sim$100 MeV to few TeV) and cosmic rays (electrons up to 20 TeV and nuclei up to $\sim$10$^{15}$ eV). The full simulation framework of GAMMA-400 is based on the Geant4 toolkit. The details of the gamma-ray reconstruction pipeline in the pre-shower and calorimeter will be outlined. The performance of GAMMA-400 (PSF, effective area) have been obtained using this framework. The most updated results on them will be shown.

astro-ph.IM↗
arXiv2015

The GAMMA-400 Space Mission

GAMMA-400 is a new space mission which will be installed on board the Russian space platform Navigator. It is scheduled to be launched at the beginning of the next decade. GAMMA-400 is designed to study simultaneously gamma rays (up to 3 TeV) and cosmic rays (electrons and positrons from 1 GeV to 20 TeV, nuclei up to 10$^{15}$-10$^{16}$ eV). Being a dual-purpose mission, GAMMA-400 will be able to address some of the most impelling science topics, such as search for signatures of dark matter, cosmic-rays origin and propagation, and the nature of transients. GAMMA-400 will try to solve the unanswered questions on these topics by high-precision measurements of the Galactic and extragalactic gamma-ray sources, Galactic and extragalactic diffuse emission and the spectra of cosmic-ray electrons + positrons and nuclei, thanks to excellent energy and angular resolutions.

astro-ph.IM↗