Direction distribution for nodal components of random band-limited functions on surfaces

Abstract

Let (M, g) be a smooth compact Riemannian surface with no boundary. Given a smooth vector field V with finitely many zeroes on M, we study the distribution of the number of tangencies to V of the nodal components of random band-limited functions. It is determined that in the high-energy limit, these obey a universal deterministic law, independent of the surface M and the vector field V , that is supported precisely on the even integers 2Z >0 .Date: October 25, 2019.