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Multi-normex distributions for the sum of random vectors. Rates of convergence
Extremes. 2023. Vol. 26. No. 3. P. 509–544.
Kratz M., Prokopenko E.
We build a sharp approximation of the whole distribution of the sum of iid heavy-tailed random vectors, combining mean and extreme behaviors. It extends the so-called ’normex’ approach from a univariate to a multivariate framework. We propose two possible multi-normex distributions, named d-Normex and MRV-Normex. Both rely on the Gaussian distribution for describing the mean behavior, via the CLT, while the difference between the two versions comes from using the exact distribution or the EV theorem for the maximum. The main theorems provide the rate of convergence for each version of the multi-normex distributions towards the distribution of the sum, assuming second order regular variation property for the norm of the parent random vector when considering the MRV-normex case. Numerical illustrations and comparisons are proposed with various dependence structures on the parent random vector, using QQ-plots based on geometrical quantiles.
Осипов Д.В., Математический сборник 2026 Т. 217 № 9 С. 130–146
Изучаются законы взаимности, связанные с комплексными линейными расслоениями на расслоениях на ориентируемые окружности. В частности, доказывается следующий закон взаимности. Пусть B – комплексное многообразие и πi:Mi→B – расслоение на ориентируемые окружности, где индекс i пробегает конечное множество. Пусть Li и Ni – комплексные линейные расслоения на каждом многообразии Mi. Закон взаимности утверждает, что сумма всех элементов (πi)∗(c1(Li)∪c1(Ni)), где (πi)∗ – ...
Added: September 3, 2026
Basalaev A., Rarovskii A., Journal of Singularities 2026 Vol. 30 P. 61–80
Saito theory associates to an isolated singularity rich structure that plays an important role in mirror symmetry. In this note we construct Saito theory for A and D type Landau-Ginzburg orbifolds. Namely, for the pairs (f,G), where f defines an isolated singularity of A and D type and G is a group of symmetries of ...
Added: September 1, 2026
Rybakov M., Shkatov D., Journal of Logic and Computation 2026 Vol. 36 No. 6 Article exag026
We prove Pi-1-1-hardness, and thus lack of recursive axiomatizability, of constant-domain modal predicate logics defined by a class of Dedekind complete linear Kripke frames containing a frame with an infinitely increasing chain of worlds. The result holds even for the language with one unary predicate letter, one propositional letter, and two individual variables. ...
Added: September 1, 2026
Селянин Ф. И., Moscow Mathematical Journal 2026 Vol. 26 No. 2 P. 167–187
Minkowski mixed volume of n subpolytopes D1,…,Dn of a polytope P⊂Rn clearly does not exceed the normalized volume n!Vol(P). Equality holds if and only if the subpolytopes are interlaced, i.e., each proper face F⊊P intersects at least dim(F)+1 of the polytopes Di. Efficiently computing mixed volumes for more general collections of subpolytopes is crucial for estimating the complexity of numerically solving polynomial systems.
Motivated by relaxing the bound dim(F)+1 to dim(F), we ...
Added: August 31, 2026
Kazaryan M., Dunin-Barkowski P., Bychkov B. et al., International Mathematics Research Notices 2026 Vol. 14 Article rnag146
We prove a recent conjecture of the fourth named author with P. Norbury that states a system of universal polynomial relations among the kappa classes on the moduli spaces of algebraic curves. The proof involves localization and materialization analysis of the spin Gromov–Witten theory of the projective line and is dictated by Z 2 -equivariant ...
Added: August 31, 2026
Kazaryan M., Dunin-Barkowski P., Bychkov B. et al., Communications in Mathematical Physics 2026 Vol. 407 No. 69
We prove that for any initial data on a genus zero spectral curve the cor responding correlation differentials of topological recursion are KP integrable. As an application we prove KP integrability of partition functions associated via ELSV-type formulas to the r-th roots of the twisted powers of the log canonical bundles ...
Added: August 31, 2026
Gromov V., Переслегин С. Б., Переслегина Е. Б. et al., СПб.: Полакс, 2026.
Механизм происходящих в мире изменений носит эволюционный, а не экологический характер. Иначе говоря, Человечество столкнулось с кризисом развития, который имеет три независимые составляющие: кризис индустриального общества (фазовый кризис), кризис научного мышления (эпистемный кризис) и кризис формата существования разума (социосистемный кризис). Доклад посвящён аспектам этого триединого кризиса и возможным путям его преодоления, не сводящимся к первичному ...
Added: August 31, 2026
Devyatov R. A., Mathematical notes 2026 Vol. 119 No. 3 P. 782–786
Let G/B be a flag variety over ℂ, where G is a simple algebraic group with a simply laced Dynkin diagram, and B is a Borel subgroup. We say that the product of classes of Schubert divisors in the Chow ring is multiplicity free if it is possible to multiply it by a Schubert class ...
Added: August 30, 2026
Bayer A., Kuznetsov A., Macrì E., Journal fuer die reine und angewandte Mathematik 2026 Vol. 2026 No. 836 P. 111–162
We give a self-contained and simplified proof of Mukai’s classification of prime Fano threefolds of index 1 and genus g ≥ 6 with at most factorial terminal singularities, and of its extension to higher dimension. ...
Added: August 30, 2026
Bayer A., Kuznetsov A., Macrì E., Compositio Mathematica 2026 Vol. 162 No. 1 P. 59–99
We give a proof of Mukai’s theorem on the existence of certain exceptional vector bundles on prime Fano threefolds. To our knowledge this is the first complete proof in the literature. The result is essential for Mukai’s biregular classification of prime Fano threefolds, and for the existence of semiorthogonal decompositions in their derived categories. Our ...
Added: August 30, 2026
Guseva L., Novikov A., Advances in Mathematics 2026 Vol. 503 Article 111211
We prove that the Kuznetsov–Polishchuk exceptional collections on rational homogeneous spaces of the symplectic groups Sp(2n,C) are full and consist of vector bundles. To achieve this, we construct several classes of complexes, which we call generalized staircase complexes, symplectic staircase complexes and secondary staircase complexes — each of which may be of independent interest. ...
Added: August 30, 2026
Polishchuk A., Rains E., Journal of the Institute of Mathematics of Jussieu 2026 Vol. 25 No. 1 P. 339–373
We prove that for every relatively prime pair of integers (d,r) with r>0, there exists an exceptional pair (O,V) on any del Pezzo surface of degree 4, such that V is a bundle of rank r and degree d. As an application, we prove that every Feigin-Odesskii Poisson bracket on a projective space can be ...
Added: August 30, 2026
Kazhdan D., Polishchuk A., Pure and Applied Mathematics Quarterly 2026 Vol. 22 No. 3 P. 1115–1166
We continue the study of automorphic functions associated with a curve C over the ring k[ε]/(ε²), where k is a finite field, begun in arXiv:2303.16259. Namely, we study an example of theta-lifting in this framework and show that it can be understood in terms of the orbit decomposition of the space of automorphic functions S(SL₂(F)\SL₂(A_C)) ...
Added: August 30, 2026
Kuznetsov A. P., Sataev I. R., Stankevich N., Chaos 2026 Vol. 36 No. 8 Article 083131
A radio-physical system, namely, a two-mode van der Pol generator, is considered. It is shown that this system demonstrates two types of chaos: with one and two zero Lyapunov exponents. The regions of the second type of chaos are surrounded by bifurcation lines of invariant tori doubling. Quasi-periodic structures of various shapes are embedded within ...
Added: August 30, 2026
Shirokov N. A., Rozenblum G., Israel Journal of Mathematics 2026 P. 1–30
We establish that a generalized H\¨older continuous function on an (m−2)-Ahlfors regular compact set in Rm can be approximated by solutions of an elliptic equation, with the rate of approximation determined by the continuity modulus of the function ...
Added: August 29, 2026
Gnetov F., Konakov V., / Series arXiv "math". 2025. No. 2512.04667.
We establish a central limit theorem, a local limit theorem, and a law of large numbers for a natural
random walk on a symmetric space M of non-compact type and rank one. This class of spaces, which
includes the complex and quaternionic hyperbolic spaces and the Cayley hyperbolic plane, generalizes
the real hyperbolic space Hn. Our approach introduces ...
Added: December 5, 2025
Glinskiy V., Artem Logachov, Logachova O. et al., Mathematics 2024 Vol. 12 No. 21 Article 3319
We investigate the asymptotic properties of the plug-in estimator for the Jeffreys divergence, the symmetric variant of the Kullback–Leibler (KL) divergence. This study focuses specifically on the divergence between discrete distributions. Traditionally, estimators rely on two independent samples corresponding to two distinct conditions. However, we propose a one-sample estimator where the condition results from a ...
Added: February 19, 2025
Logachov A.V., Mogulskii A. A., Yambartsev A. A., Siberian Electronic Mathematical Reports 2024 Vol. 21 No. 2 P. 914–926
We obtain a bound for the convergence rate in the central limit theorem for the number of triangles in a heterogeneous Erdos-Renyi graphs. Our approach is reminiscent of Hoeffding decomposition (a common technique in the theory of U-statistics). We show that the centered and normalized number of triangles asymptotically behaves as the normalized sum of ...
Added: February 19, 2025
Ulyanov V. V., Mathematics 2024 Vol. 12 No. 14 Article 2276
In 1733, de Moivre, investigating the limit distribution of the binomial distribution, was the first to discover the existence of the normal distribution and the central limit theorem (CLT). In this review article, we briefly recall the history of classical CLT and martingale CLT, and introduce new directions of CLT, namely Peng’s nonlinear CLT and ...
Added: October 31, 2024
Nikita Puchkin, Vladimir Ulyanov, Annales de l'institut Henri Poincare (B) Probability and Statistics 2023 Vol. 59 No. 3 P. 1508–1529
We show that external randomization may enforce the convergence of test statistics to their limiting distributions in particular cases. This results in a sharper inference. Our approach is based on a central limit theorem for weighted sums. We apply our method to a family of rank-based test statistics and a family of phi-divergence test statistics ...
Added: September 3, 2023
Shchegolev A., Управление большими системами: сборник трудов 2023 № 102 С. 5–14
The class of nonlinear Markov processes is characterized by the dependence of the current state of the process on its current distribution in addition to the dependence on the previous state. Due to this feature, these processes are characterized by complex limit behavior and ergodic properties, for which the usual criteria for Markov processes are ...
Added: June 12, 2023
Vedenin A., Журнал Средневолжского математического общества 2022 Т. 24 № 3 С. 280–288
This paper is devoted to a new method for constructing approximations to the solution of a parabolic partial differential equation. The Cauchy problem for the heat equation on a straight line with a variable heat conduction coefficient is considered. In this paper, a sequence of functions is constructed that converges to the solution of the ...
Added: May 18, 2023
Bobkov S., Ulyanov V. V., Theory of Probability and Its Applications 2022 Vol. 66 No. 4 P. 537–549
We give a short overview of the results related to the refined forms of the central limit theorem, with a focus on independent integer-valued random variables (r.v.'s). In the independent and non-identically distributed (non-i.i.d.) case, an approximation is then developed for the distribution of the sum by means of the Chebyshev--Edgeworth correction containing the moments ...
Added: February 22, 2022
Dragunova K., Гаращенкова А. А., Remizov I., / Series arXiv "math". 2021.
Chernoff approximations are a flexible and powerful tool of functional analysis, which can be used, in particular, to find numerically approximate solutions of some differential equations with variable coefficients. For many classes of equations such approximations have already been constructed, however, the speed of their convergence to the exact solution has not been properly studied. ...
Added: December 16, 2021