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Limit Theorems for Self-Similar Tilings
Communications in Mathematical Physics. 2013. Vol. 319. No. 3. P. 761–789.
Bufetov A. I., Solomyak B.
We study deviation of ergodic averages for dynamical systems given by self-similar tilings on the plane and in higher dimensions. The main object of our paper is a special family of finitely-additive measures for our systems. An asymptotic formula is given for ergodic integrals in terms of these finitely-additive measures, and, as a corollary, limit theorems are obtained for dynamical systems given by self-similar tilings.
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
Piontkovski D., / Series arXiv "math". 2026.
A noncommutative projective variety is defined, following Artin and Zhang, by a graded coherent algebra 𝐴. The category of coherent sheaves is then the quotient qgr(𝐴) of the category of finitely presented graded modules by the subcategory of torsion modules. We consider the categorical and polynomial entropies of the Serre twist, that is, of the ...
Added: June 23, 2026
Piontkovski D., / Series arXiv "math". 2025.
If a symmetric multilinear algebra is weakly nil, then it is Engel. This result may be regarded as an infinite-dimensional analogue of the well-known Jacobian theorem, which states that if a polynomial mapping has a polynomial inverse, then its Jacobian matrix is invertible. This refines a theorem of Gerstenhaber and partially answers a question posed ...
Added: June 23, 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
Shipilov F., Barnyakov A., Ivanov A. et al., / Series Physics "arxiv.org". 2026.
A fast simulation of the detector response is a vital task in high-energy physics (HEP). Traditional Monte-Carlo methods form the backbone of modern particle physics simulation software but are computationally expensive. We present a machine-learning-based approach to fast simulation of the Focusing Aerogel Ring Imaging Cherenkov (FARICH) detector response. Given a particle track and momentum, ...
Added: May 19, 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
Derkacheva A., Sakirkina M., Kraev G. et al., /. 2026.
Comprehensive data on natural hazards and their consequences are crucial for effective for risk assessment, adaptation planning, and emergency response. However, many countries face challenges with fragmented, inconsistent, and inaccessible data, particularly regarding local-scale events. To address this data gap in Russia, we developed an end-to-end processing pipeline that scrapes news from various online sources, ...
Added: April 28, 2026
Pilé I., Deng Y., Shchur L., / Series arXiv "math". 2026. No. 2604.10254.
We investigate the spatial overlap of successive spin configurations in Markov chain Monte Carlo simulations using the local Metropolis algorithm and the Svendsen-Wang and Wolff cluster algorithms. We examine the dynamics of these algorithms for two models in different universality classes: the Ising model and the Potts model with three components. The overlap of two ...
Added: April 20, 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
Alexander Gushchin, Valkeila E., , in: Modern problems of stochastic analysis and statistics - Selected contributions in honor of Valentin Konakov.: Heidelberg: Springer, 2017. P. 179–215.
We consider a sequence of general filtered statistical models with a finite-dimensional parameter. It is tacitly assumed that a proper rescaling of the parameter space is already done (so we deal with a local parameter) and also time rescaling is done if necessary. Our first and main purpose is to give sufficient conditions for the ...
Added: January 8, 2018
Grishunina S., , in: Book of Abstracts of the 17th Applied Stochastic Models and Data Analysis International Conference with Demographics workshop (ASMDA 2017), 6-9 june 2017, London, UK.: ISAST: International Society for the Advancement of Science and Technology, 2017. P. 89–89.
In this paper we investigate a multi-server queueing system with regenerative input flow and independent service times with finite mean. Queues with several servers are sufficiently complex but considerably interesting. There are many papers devoted to this theme. We consider queueing systems with various rules (disciplines) of the service performance: systems with a common queue ...
Added: September 5, 2017
Kelbert M., Orsingher E., Modern Stochastics: Theory and Applications 2017 Vol. 4 No. 1 P. 79–89
A random flight on a plane with non-isotropic displacements at the moments of direction changes is considered. In the case of exponentially distributed flight lengths a Gaussian limit theorem is proved for the position of a particle in the scheme of series when jump lengths and non-isotropic displacements tend to zero. If the flight lengths ...
Added: April 7, 2017
Bufetov A. I., Moscow Mathematical Journal 2014 Vol. 14 No. 2 P. 205–224
An asymptotic expansion for ergodic integrals and limit theorems are obtained for translation flows along stable foliations of pseudo-Anosov automorphisms ...
Added: October 15, 2015
А.И. Буфетов, Успехи математических наук 2013 Т. 68 № 5(413) С. 3–80
In this paper an asymptotic expansion of ergodic integrals for suspension flows over Vershik automorphisms is obtained and a limit theorem for these flows is given.
Bibliography: 49 titles. ...
Added: October 23, 2014
Vereshchagin N., , in: Descriptional Complexity of Formal Systems - 16th International Workshop, DCFS 2014, Turku, Finland, August 5-8, 2014. ProceedingsVol. 8614.: Berlin: Springer, 2014. P. 29–41.
Let ψ denote the square root of the golden ratio, ψ = ( 5 − 1)/2.
A golden triangle is any right triangle with legs of lengths a, b where
a/b = ψ. We consider tilings of the plane by two golden triangles: that
with legs 1, ψ and that with legs ψ, ψ 2 . Under some ...
Added: October 6, 2014
Bufetov A. I., Annals of Mathematics 2014 Vol. 179 No. 2 P. 431–499
The aim of this paper is to obtain an asymptotic expansion for ergodic integrals of translation ows on at surfaces of higher genus (Theorem 1) and to give a limit theorem for these ows (Theorem 2). © 2014 Department of Mathematics, Princeton University. ...
Added: February 19, 2014
Durand B., Shen A., Vereshchagin N., / Series math "arxiv.org". 2012. No. 2896.
We describe all Ammann tilings of a plane, a half-plane and a quadrant. In our description, every tiling is associated to an infinite sequence of two letters. We provide simple criteria of (a) whether a tiling associated with a sequence tiles the entire plane, a half-plane or a quadrant and (b) whether tiling associated with ...
Added: December 11, 2013
Heidelberg: Springer, 2013.
With scientific contributions by international experts
Anniversary edition for a winner of the Lenin prize
Includes interviews
The role of Yuri Vasilyevich Prokhorov as a prominent mathematician and leading expert in the theory of probability is well known. Even early in his career he obtained substantial results on the validity of the strong law of large numbers and on the ...
Added: March 12, 2013
Ivchenko G., Медведев Ю. И., Математические вопросы криптографии 2012 Т. 3 № 3 С. 21–34
Предлагается общая вероятностная модель для булевых функций от n переменных, задаваемая произвольной вероятностной мерой на множестве всех таких функций. Выводится характеристическая функция спектра Уолша случайной функции и находятся точные и асимптотические (при n→∞) распределения некоторых его характеристик для случая
параметрической меры. ...
Added: November 19, 2012