Chang, Mei-Chu; Nguyen, Hoi; Nguyen, Oanh; Vu, Van Random eigenfunctions on flat tori: universality for the number of intersections. (English) Zbl 1462.53031 Int. Math. Res. Not. 2020, No. 24, 9933-9973 (2020). Summary: We show that several statistics of the number of intersections between random eigenfunctions of general eigenvalues and a given smooth curve in flat tori are universal under various families of randomness. Cited in 5 Documents MSC: 53C21 Methods of global Riemannian geometry, including PDE methods; curvature restrictions 58J50 Spectral problems; spectral geometry; scattering theory on manifolds 35P15 Estimates of eigenvalues in context of PDEs Keywords:flat tori; Laplacian; eigenvalue; random eigenfunctions; nodal set; arithmetic random wave PDFBibTeX XMLCite \textit{M.-C. Chang} et al., Int. Math. Res. Not. 2020, No. 24, 9933--9973 (2020; Zbl 1462.53031) Full Text: DOI arXiv