1 citations · 1 across the 8 of their papers we have counts for
8 papers
Non-external Proofs of Lagrange Inversion Formula
Dominik Beck, Piotr Maćkowiak
The goal of the paper is to present two simple proofs of the Lagrange Inversion Formula for formal power series. Both proofs are non-external in the sense that they use concepts th…
When Mathematics Helps Physics: Calculation of the Integral of Kholodenko and Silagadze
Dominik Beck
In this paper, we show a physics-free derivation of a Landau-Zener type integral introduced by Kholodenko and Silagadze.
The Probability that a Random Triangle in a Cube is Obtuse
Dominik Beck
In this paper, we derive the exact formula for the probability that three randomly and uniformly selected points from the interior of the unit cube form vertices of an obtuse trian…
On Random Simplex Picking Beyond the Blashke Problem
Dominik Beck
New selected values of odd random simplex volumetric moments (moments of the volume of a random simplex picked from a given body) are derived in an exact form in various bodies in…
Mean distance in polyhedra
Dominik Beck
Given any polyhedron from which we select two random points uniformly and independently, we show that all the moments of the distance between those points can be always written in…
Efron's Mean Volume Formula in Higher Dimensions
Dominik Beck
In this short paper, an older Efron's result is extended to obtain a cutting plane integral formula for the mean volume of a random simplex in any d dimensions.
On the fourth moment of a random determinant
Dominik Beck
In this paper, we generalise the formula for the fourth moment of a random determinant to account for entries with asymmetric distribution. We also derive the second moment of a ra…
The Sixth Moment of Random Determinants
Dominik Beck, Zelin Lv, Aaron Potechin
In this paper, we determine the sixth moment of the determinant of an asymmetric random matrix where the entries are drawn independently from an arbitrary distribution…