Small Scale Equidistribution of Random Eigenbases
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]
|Collections||ANU Research Publications|
|Source:||Communications in Mathematical Physics|
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