Marcus Michelen

activity

20182021

most citedA Short Note on the Average Maximal Number of Balls in a Bin

2 citations · 3 across the 2 of their papers we have counts for

collaborators

9 papers

math.PR2021★ 1 cited

The singularity probability of a random symmetric matrix is exponentially small

Marcelo Campos, Matthew Jenssen, Marcus Michelen +1

Let $A$ be drawn uniformly at random from the set of all $n \times n$ symmetric matrices with entries in ${- 1, 1}$ . We show that \[ \mathbb{P}( \det(A) = 0 ) \leq e^{-cn},\] where…

math.PR2020

Singularity of random symmetric matrices revisited

Marcelo Campos, Matthew Jenssen, Marcus Michelen +1

Let $M_{n}$ be drawn uniformly from all $\pm 1$ symmetric $n \times n$ matrices. We show that the probability that $M_{n}$ is singular is at most $exp (- c (n lo g n)^{1/2})$ , which repre…

math.PR2020

Real roots near the unit circle of random polynomials

Marcus Michelen

Let $f_{n} (z) = \sum_{k = 0}^{n} ε_{k} z^{k}$ be a random polynomial where $ε_{0}, \dots, ε_{n}$ are i.i.d. random variables with $E ε_{1} = 0$ an…

math.PR2020

Random polynomials: the closest roots to the unit circle

Marcus Michelen, Julian Sahasrabudhe

Let $f = \sum_{k = 0}^{n} ε_{k} z^{k}$ be a random polynomial, where $ε_{0}, \dots, ε_{n}$ are iid standard Gaussian random variables, and let $ζ_{1}, \dots, ζ_{n}$ de…

math.CO2020

Asymptotic bounds on graphical partitions and partition comparability

Stephen Melczer, Marcus Michelen, Somabha Mukherjee

An integer partition is called graphical if it is the degree sequence of a simple graph. We prove that the probability that a uniformly chosen partition of size $n$ is graphical de…

math.CA2019

A characterization of polynomials whose high powers have non-negative coefficients

Marcus Michelen, Julian Sahasrabudhe

Let $f \in R [x]$ be a polynomial with real coefficients. We say that $f$ is eventually non-negative if $f^{m}$ has non-negative coefficients for all sufficiently large $m \i…