In the recent paper Bürgisser and Lerario (Journal für die reine und angewandte Mathematik (Crelles J), 2016) introduced a geometric framework for a probabilistic study of real Schubert Problems. They denoted by δk,n the average number of projective k-planes in RPn that intersect (k+1)(n−k) many random, independent and uniformly distributed linear projective subspaces of dimension n−k−1. They called δk,n the expected degree of the real Grassmannian G(k,n) and, in the case k=1, they proved that: δ1,n=83π5/2⋅(π24)n⋅n−1/2(1+O(n−1)). Here we generalize this result and prove that for every fixed integer k>0 and as n→∞, we have δk,n=ak⋅(bk)n⋅n−k(k+1)4(1+O(n−1)) where ak and bk are some (explicit) constants, and ak involves an interesti...
AbstractThe aim of this paper is the study of a rate of convergence of Poisson integrals for Hermite...
Following attempts at an analytic proof of the Pentagonal Number Theorem, we report on the discovery...
Let Amp,r(n) be the best constant that fulfills the following inequality: for every m-homogeneous po...
Motivated by questions in real enumerative geometry (Borcea et al., in Discrete Comput Geom 35(2):28...
2000 Mathematics Subject Classification: 05A16, 05A17.Let Xm,n denote the number of parts of multipl...
We demonstrate that the phenomenon of popular differences (aka the phenomenon of large intersections...
Asymptotic formulas for large-deviation probabilities of a ladder height in a random walk generated...
Let {φi}∞i=0 be a sequence of orthonormal polynomials on the unit circle with respect to a positive ...
In this article we continue formalizing probability and randomness started in [13], where we formali...
In this paper, we establish asymptotics of radial limits for certain functions of Wright. These fun...
Given a probability space (Ω, A, P), a separable metric space X, and a random-valued vector function...
Let $k\ge 2$ be a fixed integer. We consider sums of type $\sum_{n_1\cdots n_k\le x} F(n_1,\ldots,n_...
Given an i.i.d. sequence $\{A_n(\omega)\}_{n\ge 1}$ of invertible matrices and a random matrix $B(\o...
AbstractWe strengthen a theorem of Kuijlaars and Serra Capizzano on the distribution of zeros of a s...
AbstractIn this paper the asymptotic behavior of Szász operators for locally bounded functions f is ...
AbstractThe aim of this paper is the study of a rate of convergence of Poisson integrals for Hermite...
Following attempts at an analytic proof of the Pentagonal Number Theorem, we report on the discovery...
Let Amp,r(n) be the best constant that fulfills the following inequality: for every m-homogeneous po...
Motivated by questions in real enumerative geometry (Borcea et al., in Discrete Comput Geom 35(2):28...
2000 Mathematics Subject Classification: 05A16, 05A17.Let Xm,n denote the number of parts of multipl...
We demonstrate that the phenomenon of popular differences (aka the phenomenon of large intersections...
Asymptotic formulas for large-deviation probabilities of a ladder height in a random walk generated...
Let {φi}∞i=0 be a sequence of orthonormal polynomials on the unit circle with respect to a positive ...
In this article we continue formalizing probability and randomness started in [13], where we formali...
In this paper, we establish asymptotics of radial limits for certain functions of Wright. These fun...
Given a probability space (Ω, A, P), a separable metric space X, and a random-valued vector function...
Let $k\ge 2$ be a fixed integer. We consider sums of type $\sum_{n_1\cdots n_k\le x} F(n_1,\ldots,n_...
Given an i.i.d. sequence $\{A_n(\omega)\}_{n\ge 1}$ of invertible matrices and a random matrix $B(\o...
AbstractWe strengthen a theorem of Kuijlaars and Serra Capizzano on the distribution of zeros of a s...
AbstractIn this paper the asymptotic behavior of Szász operators for locally bounded functions f is ...
AbstractThe aim of this paper is the study of a rate of convergence of Poisson integrals for Hermite...
Following attempts at an analytic proof of the Pentagonal Number Theorem, we report on the discovery...
Let Amp,r(n) be the best constant that fulfills the following inequality: for every m-homogeneous po...