Related papers: Extremal numbers and multi-parametric geometry of …
In this paper we develop new extremal principles in variational analysis that deal with finite and infinite systems of convex and nonconvex sets. The results obtained, unified under the name of tangential extremal principles, combine primal…
Extreme value distributions are routinely employed to assess risks connected to extreme events in a large number of applications. They typically are two- or three- parameter distributions: the inference can be unstable, which is…
We study equivariant geometry and rationality of moduli spaces of points on the projective line, for twists associated with permutations of the points.
This paper develops new extremal principles of variational analysis that are motivated by applications to constrained problems of stochastic programming and semi-infinite programming without smoothness and/or convexity assumptions. These…
We calculated the exact value and found the polynomial of the best weighted polynomial approximation of the kernels of the form $\frac {A+Bx}{(x^2+\lambda^2)^2}$, where $A,B\in {\mathbb R}$, $\lambda>0$ in the mean-square metric.
Deng (arXiv:math/9812082) gave an asymptotic formula for the number of rational points on a weighted projective space over a number field with respect to a certain height function. We prove a generalization of Deng's result involving a…
We study the extremes for a class of a symmetric stable random fields with long range dependence. We prove functional extremal theorems both in the space of sup measures and in the space of cadlag functions of several variables. The limits…
In this paper we introduce new notions of local extremality for finite and infinite systems of closed sets and establish the corresponding extremal principles for them called here rated extremal principles. These developments are in the…
Extreme value theory for univariate and low-dimensional observations has been explored in considerable detail, but the field is still in an early stage regarding high-dimensional settings. This paper focuses on H\"usler-Reiss models, a…
This is a survey of old and new problems and results in additive number theory.
Weighted cone-volume functionals are introduced for the convex polytopes in $\mathbb{R}^n$. For these functionals, geometric inequalities are proved and the equality conditions are characterized. A variety of corollaries are derived,…
In this paper we discuss the explicit solution of certain extremal problems in Bergman spaces. In order to do this, we develop methods to calculate the Bergman projections of various functions. As a special case, we deal with canonical…
We show that on most of the hyperbolic simply connected domains the weighted bounded rational approximation in a natural sup norm is possible only for a very sparse set of holomorphic functions (in contrast to integral approximation). The…
Works, briefly surveyed here, are concerned with two basic methods: Maximum Probability and Bayesian Maximum Probability; as well as with their asymptotic instances: Relative Entropy Maximization and Maximum Non-parametric Likelihood.…
This paper studies the problem of identifying directions of axial symmetry in multivariate distributions. Theoretical results are derived on how the measure or cardinality of the set of symmetry directions relates to spherical symmetry. The…
In this work, we deal with extreme value theory in the context of continued fractions using techniques from probability theory, ergodic theory and real analysis. We give an upper bound for the rate of convergence in the Doeblin-Iosifescu…
Extremality and irreducibility constitute fundamental concepts in mathematics, particularly within tropical geometry. While extremal decomposition is typically computationally hard, this article presents a fast algorithm for identifying the…
In this work, we study the existence and nonexistence of solution for strongly coupled elliptic systems to m-parameters.
Our contribution is to widen the scope of extreme value analysis applied to discrete-valued data. Extreme values of a random variable $X$ are commonly modeled using the generalized Pareto distribution, a method that often gives good results…
We suggest approximating the distribution of the sum of independent and identically distributed random variables with a Pareto-like tail by combining extreme value approximations for the largest summands with a normal approximation for the…