arXiv subjects

Tatiana Moseeva

Publications and source records attributed to Tatiana Moseeva.

4 recordsLinked to original sources

arXiv2024

Mixed random beta-polytopes

In this paper, we generalize the result on the average volume of random polytopes with vertices following beta distributionsto the case of non-identically distributed vectors. Specifically,we consider the convex hull of independent random vectors in $\mathbb{R}^d$, where each vector follows a beta distribution with potentially different parameters. We derive an expression for the expected volume of these generalized beta--polytopes. Additionally, we compute the expected value of a functional introduced by Wieacker, which involves the distance of facets from the origin and their volumes.Our results extend the findings of Kabluchko, Temesvari,and Thäle. Key techniques used in the proofs include the Blaschke--Petkantschin formula, Kubota's formula, and projections of beta distributed random vectors.

math.PR↗

arXiv2022

Integral Identities for the boundary of a convex body

We present the multidimensional versions of the Pleijel and Ambartzumian--Pleijel identities. We also obtain the generalization of both the Blaschke--Petkantschin and Zähle formulae considering the case when some points are chosen inside the convex body and some on the boundary. Moreover, a version of the Zähle formula for the polytopes is derived.

math.MG↗

arXiv2020

Distribution of the Volume of Weighted Gaussian Simplex

Let $X_0, \ldots, X_l$ be independent standard Gaussian vectors in $\mathbb{R}^d$ such that $l \leqslant d$. We derive an explicit formula for the distribution of the volume of weighted Gaussian simplex without the origin -- $l$-dimensional simplex $\mathrm{conv}(σ_0X_0, \ldots, σ_lX_l)$ ($σ_0, \ldots, σ_l > 0$).

math.PR↗

arXiv2020

Random sections of spherical convex bodies

Let $K\subset\mathbb S^{d-1}$ be a convex spherical body. Denote by $Δ(K)$ the distance between two random points in $K$ and denote by $σ(K)$ the length of a random chord of $K$. We explicitly express the distribution of $Δ(K)$ via the distribution of $σ(K)$. From this we find the density of distribution of $Δ(K)$ when $K$ is a spherical cap.

math.PR↗