5 papers · 1 filter
Root Dynamics of Differentiated Polynomials with Rotationally Invariant Structure
Joseph Najnudel, Truong Vu
The dynamics of polynomial roots under repeated differentiation has recently been conjectured to converge to a limiting measure governed by specific nonlinear PDEs, the conjectures…
The Fourier coefficients of the critical holomorphic multiplicative chaos
Christopher Atherfold, Joseph Najnudel
The holomorphic multiplicative chaos (HMC) is a holomorphic analogue of the Gaussian multiplicative chaos. It arises naturally as the limit in large matrix size of the characterist…
Dynamics of rotationally invariant polynomial root sets under iterated differentiations
André Galligo, Joseph Najnudel, Truong Vu
We associate to an -sample of a given rotationally invariant probability measure with compact support in the complex plane, a polynomial with roots given by the sam…
Dynamics of roots of randomized derivative polynomials
André Galligo, Joseph Najnudel
In this paper, we study the asymptotic macroscopic behavior of the root sets of iterated, randomized derivatives of polynomials. The randomization depend on a parameter of inverse…
The Fourier coefficients of the holomorphic multiplicative chaos in the limit of large frequency
Joseph Najnudel, Elliot Paquette, Nick Simm +1
The holomorphic multiplicative chaos (HMC) is a holomorphic analogue of the Gaussian multiplicative chaos. It arises naturally as the limit in large matrix size of the characterist…