Marcus Michelen

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20242026

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math.PR2026

A simple proof of local universality for roots of Kac polynomials

Marcus Michelen, Oren Yakir

Let $f_{n}$ be a random polynomial of degree $n$ with i.i.d. mean-zero and finite variance random coefficients. It is well known that the roots of $f_{n}$ cluster uniformly around the…

math.PR2025

Convergent points for random power series on the unit circle

Marcus Michelen, Mehtaab Sawhney

Consider a random power series of the form $P (z) = \sum_{n \geq 1} ε_{n} a_{n} z^{n}$ where $a_{n} \in C$ are deterministic and $ε_{n}$ are chosen independently…

math.PR2025

Law of large numbers for the discriminant of random polynomials

Marcus Michelen, Oren Yakir

Let $f_{n}$ be a random polynomial of degree $n$ , whose coefficients are independent and identically distributed random variables with mean-zero and variance one. Let $I^ (f_{n})$ denot…

math.PR2025

Limit law for root separation in random polynomials

Marcus Michelen, Oren Yakir

Let $f_{n}$ be a random polynomial of degree $n \geq 2$ whose coefficients are independent and identically distributed random variables. We study the separation distances between roots…

math.PR2025

On random locally flat-foldable origami

Thomas C. Hull, Marcus Michelen, Corrine Yap

We develop a theory of random flat-foldable origami. Given a crease pattern, we consider a uniformly random assignment of mountain and valley creases, conditioned on the assignment…

math.PR2024

Fluctuations in the logarithmic energy for zeros of random polynomials on the sphere

Marcus Michelen, Oren Yakir

Smale's Seventh Problem asks for an efficient algorithm to generate a configuration of $n$ points on the sphere that nearly minimizes the logarithmic energy. As a candidate startin…