Counting nodal domains
Abstract
We consider the nodal domains of Gaussian random waves in two dimensions. We present a method to calculate the distribution of the number of nodal domains and the average connectivity with the help of auxiliary Potts-spins. An analytical approach could be helpful to decide whether the pattern of nodal domains belongs to the universality class of short-ranged percolation. This is not completely evident since we find (weak) long-ranged correlations between distant avoided nodal intersections.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.