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 2023 · math.PRShow all

3 papers · 2 filters

math.PR2023

On random polynomials with an intermediate number of real roots

Marcus Michelen, Sean O'Rourke

For each $α \in (0, 1)$ , we construct a bounded monotone deterministic sequence $(c_{k})_{k \geq 0}$ of real numbers so that the number of real roots of the random polynomial $f_n(z)…

math.PR2023

Almost sure behavior of the zeros of iterated derivatives of random polynomials

Marcus Michelen, Xuan-Truong Vu

Let $Z_{1}, Z_{2}, \dots$ be independent and identically distributed complex random variables with common distribution $μ$ and set $P_{n} (z) := (z - Z_{1}) \dots (z - Z_{n}) .$ Recentl…

math.PR2023

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…