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Small Scale Equidistribution of Random Eigenbases

Han, Xiaolong


We investigate small scale equidistribution of random orthonormal bases of eigenfunctions (i.e., eigenbases) on a compact manifold M. Assume that the group of isometries acts transitively on M and the multiplicity mλ of eigenfrequency λ tends to infinity at least logarithmically as λ → ∞. We prove that, with respect to the natural probability measure on the space of eigenbases, almost surely a random eigenbasis is equidistributed at small scales; furthermore, the scales depend on the...[Show more]

CollectionsANU Research Publications
Date published: 2016
Type: Journal article
Source: Communications in Mathematical Physics
DOI: 10.1007/s00220-016-2597-8


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