期刊
INTERNATIONAL MATHEMATICS RESEARCH NOTICES
卷 2019, 期 9, 页码 2661-2689出版社
OXFORD UNIV PRESS
DOI: 10.1093/imrn/rnx197
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资金
- European Research Council under the European Unions [335141]
- Engineering and Physical Sciences Research Council (EPSRC) Fellowship [EP/M002896/1]
- EPSRC [EP/M002896/1] Funding Source: UKRI
- European Research Council (ERC) [335141] Funding Source: European Research Council (ERC)
Random plane wave is conjectured to be a universal model for high-energy eigenfunctions of the Laplace operator on generic compact Riemannian manifolds. This is known to be true on average. In the present paper we discuss one of important geometric observable: critical points. We first compute one-point function for the critical point process, in particular we compute the expected number of critical points inside any open set. After that we compute the short-range asymptotic behaviour of the two-point function. This gives an unexpected result that the second factorial moment of the number of critical points in a small disc scales as the fourth power of the radius.
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