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Fractional smoothness of images of logarithmically concave measures under polynomials
Journal of Mathematical Analysis and Applications. 2018. Vol. 462. No. 1. P. 390–406.
We show that a measure on the real line, that is the image of a log-concave measure under a polynomial of degree d, possesses a density from the Nikolskii–Besov class of fractional order 1/d. This result is used to prove an estimate for the total variation distance between such measures in terms of the Fortet–Mourier distance.
Levashev V., / Series arXiv "math". 2026. No. 2609.06010.
We prove that continuous A-bilinear pairings on the ring of Laurent series that are invariant under continuous automorphisms coincide, up to a constant, with the pairing given by the residue of a differential form over any commutative associative ring with identity. ...
Added: September 24, 2026
Pyatov P. N., Pivovarov P. A., / Series math "arxiv.org". 2026. No. 2609.06274.
We investigate a special ansats that allows for an iterative solution of the constant Yang-Baxter equation. Testing this ansatz, we construct four sequences of the constant R-matrices. In each sequence the R-matrices act on the tensor squares of vector spaces of linearly growing dimensions. Each R-matrix also depends on a single complex parameter.
By analyzing the ...
Added: September 24, 2026
Medvedev V., / Series arXiv "math". 2026.
We study complete static manifolds with boundary admitting a nowhere-vanishing static potential. Our main result shows that, under a natural lower bound relating the scalar curvature and the boundary mean curvature, a simple static manifold with boundary must in fact have positive scalar curvature, negative boundary mean curvature, and be compact; we also obtain explicit ...
Added: September 19, 2026
Poddiakov A., / Series Social Science Research Network "Social Science Research Network". 2026. No. 7437658.
Clarity of knowledge and reasoning is necessary in many cases. Yet vagueness in scientific thinking related to surprise, curiosity, "ability to engage with not-knowing" (de Freitas) and abductive reasoning is also a crucially important source of scientific creativity which supplements combinatorial logic when dealing with the already known. Starting from studies by C. S. Peirce ...
Added: September 15, 2026
Glutsyuk A., / Series arXiv "math". 2026.
B.Josephson (Nobel Prize, 1973) predicted a tunnelling effect for a system of two superconductors separated by a narrow dielectric (such a system is called Josephson junction): existence of a supercurrent through it and equations governing it. The overdamped Josephson junction is modeled by the family of differential equations on the 2-torus, dθdτ=1ω(cosθ+B+Acosτ), which is known as ...
Added: September 8, 2026
Pochinka O., Shmukler V., / Series math.RT "arXiv:1808.06395 [math.RT]". 2026.
Anosov flows have a long and rich history, firstly motivated by the
study of geodesic flows in negative curvature surface by Anosov and Sinai.
Not every closed manifold admits an Anosov flow for well-known reasons:
the fundamental group of a 3-manifold M admitting an Anosov flow must
have exponential growth, and M must be universally covered by R3. Nevertheless,
there ...
Added: August 31, 2026
Loubenets E. R., / Series arxiv.org "quant-ph". 2026. No. 2607.18050.
In many quantum applications it is important to know whether or not a Bell nonlocal two-qudit state exhibits its nonlocality under correlation scenarios with some given numbers S1,S2≥1 of generalized quantum measurements at two sites. In the present article, we find analytically a new general locality condition sufficient for a nonseparable Werner state with a ...
Added: July 21, 2026
Bolbachan V., / Series math "arxiv.org". 2024.
Chow polylogarithms are some special functions arising in explicit description of the Beilinson regulator map. The most interesting functional equation for this function reflects its vanishing on the boundary in the Bloch's cycle complex. We show that this functional equation formally follows from more simple ones, namely skew-symmetry, functoriality and multiplicativity.
To prove this, we study ...
Added: July 16, 2026
Bolbachan V., / Series math "arxiv.org". 2024.
Let K be a field of characteristic zero. We prove that its motivic cohomology in degree m−1 and weight m is rationally isomorphic to the cohomology of the polylogarithmic complex. This gives a partial extension of A. Suslin theorem describing the indecomposable K3 of a field. ...
Added: July 16, 2026
Panov V., Ryabchenko A., / Series arXiv "stat.ME". 2026. No. 2607.05048.
This paper investigates the problem of statistical inference for a mixture distribution consisting of a discrete and a continuous component, with a particular focus on the class of rational-infinitely divisible distributions. We consider non-parametric estimation of both components of the mixture as well as the quasi-L{é}vy measure, assuming that the mixture belongs to the class ...
Added: July 9, 2026
Konakov V., Kucher D., Mammen E., / Series arXiv "math". 2026. No. 2606.11142v1.
In this paper, we construct strong approximations for discrete-time Markov chains weakly converging to continuous diffusion processes, as well as for their perturbed counterparts. Under the assumption of bounded coefficients, we construct closely coupled versions of these processes on a shared probability space. In particular, for both non-degenerate and degenerate cases, we maximize the probability ...
Added: June 11, 2026
Dorovskiy A., / Series arXiv "math". 2026.
In this paper the structural stability of generic families of vector fields of the PC-HC class on the two-dimensional sphere is proved. A classification of these families up to moderate equivalence in neighborhoods of their large bifurcation supports is presented, based on such invariants as the configuration and the characteristic set. The realization lemma is proved. ...
Added: May 14, 2026
Taletskii D., / Series arXiv "math". 2026.
A vertex subset of a graph is called a \textit{distance-$k$ independent set} if the distance between any two of its distinct vertices is at least $k + 1$. For all $n,k \geq 1$, we determine the minimum possible number of inclusion-wise maximal distance-$k$ independent sets among all $n$-vertex trees. It equals~$n$ if $n \leq k ...
Added: May 1, 2026
Ovcharenko M., / Series arXiv "math". 2026.
We introduce an explicit class of tempered Laurent polynomials in the sense of Villegas and Doran--Kerr in n⩽4 variables including all Landau--Ginzburg models for smooth Fano threefolds with very ample anticanonical class. We check that it contains Landau--Ginzburg models for various Fano fourfolds which are complete intersections in smooth toric varieties and Grassmannians of planes, ...
Added: April 30, 2026
Zlotnik Alexander, / Series arXiv "math". 2026. No. 2602.03481v1.
We deal with the global in time weak solutions to the 1D compressible Navier-Stokes system of equations for large discontinuous initial data and nonhomogeneous boundary conditions of three standard types. We prove the Lipschitz-type continuous dependence of the solution $(\eta,u,\theta)$, in a norm slightly stronger than $L^{2,\infty}(Q)\times L^2(Q)\times L^2(Q)$, on the initial data $(\eta^0,u^0,e^0)$ in a ...
Added: April 18, 2026
Medvedev V., / Series arXiv "math". 2026.
We investigate the interplay between the dimension of the space of static potentials and the geometric and topological structure of the underlying static three-manifold. A partial classification of boundaryless static manifolds is obtained in terms of this dimension. We also treat the case of static manifolds with boundary. In particular, we prove that if a ...
Added: April 3, 2026
Kosov E., Zhukova A., Stochastic Processes and their Applications 2024 Vol. 170 Article 104279
The paper studies upper bounds for the total variation distance between the distributions of two polynomials of a special form in random vectors satisfying the Doeblin-type condition. Our approach is based on the recent results concerning the Nikolskii–Besov-type smoothness of the distribution densities of polynomials in logarithmically concave random vectors. The main results of the ...
Added: February 7, 2025
Kosov E., Mathematical notes 2023 Vol. 114 No. 5 P. 862–874
The paper studies the regularity properties of images of Fomin differentiable measures under mappings in Sobolev classes. The obtained results generalize recently obtained bounds in Gaussian case to more abstract settings. ...
Added: February 7, 2025
Bogachev V., Труды Математического института им. В.А. Стеклова РАН 2023 Т. 323 С. 65–86
Обсуждаются различные определения классов Соболева и Бесова на бесконечномерных пространствах. Дан обзор результатов о совпадении некоторых таких классов, получен ряд новых результатов. ...
Added: February 24, 2024
Afonin K., Bogachev V., Communications on Pure and Applied Analysis 2023 Vol. 22 No. 2 P. 597–612
We study two topologies τKR and τK on the space of measures on a completely regular space generated by Kantorovich-Rubinshtein and Kantorovich seminorms analogous to their classical norms in the case of a metric
space. The Kantorovich-Rubinshtein topology coincides with the weak topology on nonnegative measures and on bounded uniformly tight sets of measures. A sufficient condition is ...
Added: December 14, 2023
Kelbert M., Сухов Ю. М., Известия Саратовского университета. Новая серия. Серия: Математика. Механика. Информатика 2023 Vol. 23 No. 4 P. 422–434
We present a number of low and upper bounds for L\эevy – ´Prokhorov, Wasserstein, Frechet, and Hellinger distances between ´ probability distributions of the same or different dimensions. The weighted (or context-sensitive) total variance and Hellinger distances are introduced. The upper and low bounds for these weighted metrics are proved. The low bounds for the ...
Added: October 29, 2023
Kelbert M., Analytics 2023 Vol. 2 No. 1 P. 225–245
We present a number of upper and lower bounds for the total variation distances between
the most popular probability distributions. In particular, some estimates of the total variation
distances in the cases of multivariate Gaussian distributions, Poisson distributions, binomial distributions,
between a binomial and a Poisson distribution, and also in the case of negative binomial
distributions are given. Next, ...
Added: March 1, 2023
Bogachev V., Shaposhnikov A. V., Wang F. -., Communications in Contemporary Mathematics 2022 Vol. 24 No. 5 Article 2150027
New Sobolev-Kantorovich type inequalities for diffusion semigroups are obtained. ...
Added: November 14, 2022
Kosov E., Функциональный анализ и его приложения 2022 Т. 56 № 2 С. 29–38
В работе исследуются плотности мер, являющихся образами стандартной гауссовской меры на R^n при полиномиальных отображениях, причем предполагается, что общая степень многочлена фиксирована, а каждая переменная входит в его одночлены в степенях, ограниченных другим фиксированным числом. ...
Added: June 1, 2022