2 papers
math.NA2025
Discrete-to-continuum convergence of the density of states for Mathieu's equation
Peter Hofhansel, Alexander B. Watson
The density of states of a self-adjoint operator generalizes the eigenvalue distribution of a Hermitian matrix. We prove convergence of the density of states for a tight-binding mo…
math.PR2025
Growth-fragmentations, Brownian cone excursions and SLE(6) explorations of a quantum disc
William Da Silva, Ellen Powell, Alexander Watson
The aim of this article is to present a growth-fragmentation process naturally embedded in a Brownian excursion from boundary to apex in a cone of angle . This growth-fragme…