Marcus Michelen

activity

20182026

most citedCentral limit theorems and the geometry of polynomials

16 citations · 27 across the 24 of their papers we have counts for

collaborators

Showing 2020Show all

4 papers · 1 filter

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★ 2 cited

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…