On the nodal volume associated with random linear combinations of Laplace eigenfunctions

Abstract: We will study the high energy asymptotic behavior of the nodal volume associated with random linear combinations of Laplace eigenfunctions in various geometric contexts. In particular, we will show the almost sure and expected asymptotics are in some way universal, i.e. they do not depend on the base manifold, nor on the particular choice of random coefficients. The talk will be based on joined works with G. Poly and L. Gass.

differential geometryprobability

Audience: advanced learners

Young Researchers between Geometry and Stochastic Analysis 2021