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math.AP2016
Distribution of the nodal sets of eigenfunctions on analytic manifolds
Xiaolong Han
The nodal set of the Laplacian eigenfunction has co-dimension one and has finite hypersurface measure on a compact Riemannian manifold. In this paper, we investigate the distributi…
math.SP2016
Equidistribution of random waves on small balls
Xiaolong Han, Melissa Tacy
In this paper, we investigate the small scale equidistribution properties of randomised sums of Laplacian eigenfunctions (i.e. random waves) on a compact manifold. We prove small s…