Dmitry Belyaev (Oxford)
Geometry of random eigenfunctions of Laplacian
Abstract:
Random eigenfunctions of Lapalcian provide a model for
"typical" high-energy eigenfunctions of the Laplace operator in generic
domains. In this talk we will discuss random plane waves that could be
thought of as random linear combination of all possible plane waves with
the same energy. We will look at the geometric properties of these
random functions such as topology and geometry of nodal domains and
nodal lines. In particular we will show that nodal domains of any given
topological structure or with any given area occur with positive density.