Fluctuations of the Euler-Poincaré characteristic for random spherical harmonics
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- by V. Cammarota, D. Marinucci and I. Wigman PDF
- Proc. Amer. Math. Soc. 144 (2016), 4759-4775 Request permission
Abstract:
In this short note, we build upon recent results from our earlier paper to present a precise expression for the asymptotic variance of the Euler-Poincaré characteristic for the excursion sets of Gaussian eigenfunctions on $\mathcal {S}^2$; this result can be written as a second-order Gaussian kinematic formula for the excursion sets of random spherical harmonics. The covariance between the Euler-Poincaré characteristics for different level sets is shown to be fully degenerate; it is also proved that the variance for the zero level excursion sets is asymptotically of smaller order.References
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Additional Information
- V. Cammarota
- Affiliation: Department of Mathematics, Università degli Studi di Roma Tor Vergata, 00133 Rome, Italy
- MR Author ID: 829478
- Email: cammarot@mat.uniroma2.it
- D. Marinucci
- Affiliation: Department of Mathematics, Università degli Studi di Roma Tor Vergata, 00133 Rome, Italy
- MR Author ID: 656088
- Email: marinucc@mat.uniroma2.it
- I. Wigman
- Affiliation: Department of Mathematics, King’s College London, Strand, London WC2 2LS, England
- MR Author ID: 751303
- ORCID: 0000-0002-6152-4743
- Email: igor.wigman@kcl.ac.uk
- Received by editor(s): April 8, 2015
- Received by editor(s) in revised form: December 22, 2015
- Published electronically: August 1, 2016
- Additional Notes: The first and second author’s research was supported by ERC grant No. 277742
The third author’s research was supported by ERC grant No. 335141 - Communicated by: Mark M. Meerschaert
- © Copyright 2016 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 144 (2016), 4759-4775
- MSC (2010): Primary 33C55, 42C10, 60D05, 60B10, 60G60
- DOI: https://doi.org/10.1090/proc/13299
- MathSciNet review: 3544528