arXiv subjects

Dimitris Askitis

Publications and source records attributed to Dimitris Askitis.

4 recordsLinked to original sources

arXiv2021

Ratios of Entire functions and generalized Stieltjes functions

Monotonicity properties of the ratio $$ \log \frac{f(x+a_1)\cdots f(x+a_n)}{f(x+b_1)\cdots f(x+b_n)}, $$ where $f$ is an entire function are investigated. Earlier results for Euler's gamma function and other entire functions of genus 1 are generalised to entire functions of genus $p$ with negative zeros. Derivatives of order comparable to $p$ of the expression above are related to generalised Stieltjes functions of order $p+1$. Our results are applied to the Barnes multiple gamma functions. We also show how recent results on the behaviour of Euler's gamma function on vertical lines can be sharpened and generalised to functions of higher genus. Finally a connection to the so-called Prouhet-Tarry-Escott problem is described.

math.CA↗

arXiv2017

Logarithmic concavity of the inverse incomplete beta function with respect to parameter

The beta distribution is a two-parameter family of probability distributions whose distribution function is the (regularised) incomplete beta function. In this paper, the inverse incomplete beta function is studied analytically as univariate function of the first parameter. Monotonicity, limit results and convexity properties are provided. In particular, logarithmic concavity of the inverse incomplete beta function is established. In addition, we provide monotonicity results on inverses of a larger class of parametrised distributions that may be of independent interest.

math.CA↗

arXiv2017

A strong collapse increasing the geometric simplicial Lusternik-Schnirelmann category

In [3], after defining notions of LS category in the simplicial context, the authors show that the geometric simplicial LS category is non-decreasing under strong collapses. However, they do not give examples where it increases strictly, but they conjecture that such an example should exist, and thus that the geometric simplicial LS category is not strong homotopy invariant. The purpose of this note is to provide with such an example. We construct a simplicial complex whose simplicial and geometric simplicial LS categories are different, and using this, we provide an example of a strong collapse that increases the geometric simplicial LS category, thus settling the geometric simplicial LS category not being strong homotopy invariant.

math.CO↗

arXiv2016

Asymptotic expansions of the inverse of the Beta distribution

In this work in progress, we study the asymptotic behaviour of the $p$-quantile of the Beta distribution, i.e. the quantity $q$ defined implicitly by $\int_0^q t^{a - 1} (1 - t)^{b - 1} \text{d} t = p B (a, b)$, as a function of the first parameter $a$. In particular, we derive asymptotic expansions of and $q$ and its logarithm at $0$ and $\infty$. Moreover, we provide some relations between Bell and N{\o}rlund Polynomials, a generalisation of Bernoulli numbers. Finally, we provide Maple and Sage algorithms for computing the terms of the asymptotic expansions.

math.CA↗