5 papers
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…
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 samp…
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…
Anti-concentration applied to roots of randomized derivatives of polynomials
André Galligo, Joseph Najnudel, Truong Vu
Let be a random set of points and let be its \emph{empirical measure}: Let $$P_n(z) := (z -…
Direct Observation of Exceptional Points in Photonic Crystal by Cross-Polarization Imaging in Momentum Space
Viet Anh Nguyen, Viet Hoang Le, Loïc Malgrey +8
This study explores exceptional points (EPs) in photonic crystals (PhCs) and introduces a novel method for their single-shot observation. Exceptional points are spectral singularit…