Tangent nodal sets for random spherical harmonics

2018/09/05 by Eswarathasan, Suresh
#Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1809.01595

Abstract

In this note, we consider a fixed vector field V on S² and study the distribution of points which lie on the nodal set (of a random spherical harmonic) where V is also tangent. We show that the expected value of the corresponding counting function is asymptotic to the eigenvalue with a leading coefficient that is independent of the vector field V. This demonstrates, in some form, a universality for vector fields up to lower order terms.

Related

• On the correlation between nodal and boundary lengths for random\n spherical harmonics
• On the universality of the Nazarov-Sodin constant
• On the correlation between critical points and critical values for random spherical harmonics
• On the Correlation of Critical Points and Angular Trispectrum for Random\n Spherical Harmonics
• Moderate Deviation estimates for Nodal Lengths of Random Spherical Harmonics