High-frequency asymptotics for Lipschitz–Killing curvatures of excursion sets on the sphere
(2016) In Annals of Applied Probability 26(1). p.462-506- Abstract
- In this paper, we shall be concerned with geometric functionals and excursion probabilities for some nonlinear transforms evaluated on Fourier components of spherical random fields. In particular, we consider both random spherical harmonics and their smoothed averages, which can be viewed as random wavelet coefficients in the continuous case. For such fields, we consider smoothed polynomial transforms; we focus on the geometry of their excursion sets, and we study their asymptotic behaviour, in the high-frequency sense. We focus on the analysis of Euler–Poincaré characteristics, which can be exploited to derive extremely accurate estimates for excursion probabilities. The present analysis is motivated by the investigation of asymmetries... (More)
- In this paper, we shall be concerned with geometric functionals and excursion probabilities for some nonlinear transforms evaluated on Fourier components of spherical random fields. In particular, we consider both random spherical harmonics and their smoothed averages, which can be viewed as random wavelet coefficients in the continuous case. For such fields, we consider smoothed polynomial transforms; we focus on the geometry of their excursion sets, and we study their asymptotic behaviour, in the high-frequency sense. We focus on the analysis of Euler–Poincaré characteristics, which can be exploited to derive extremely accurate estimates for excursion probabilities. The present analysis is motivated by the investigation of asymmetries and anisotropies in cosmological data. The statistics we focus on are also suitable to deal with spherical random fields which can only be partially observed, the canonical example being provided by the masking effect of the Milky Way on Cosmic Microwave Background (CMB) radiation data.
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Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/f9948ed9-92ca-416b-ad35-fca5e3915ca5
- author
- Vadlamani, Sreekar LU and Marinucci, Domenico
- publishing date
- 2016
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- high-frequency asymptotics, spherical random fields, Minkowski functionals, excursion sets, Gaussian subordination, 60G60, 62M15, 53C65, 42C15
- in
- Annals of Applied Probability
- volume
- 26
- issue
- 1
- pages
- 45 pages
- publisher
- Institute of Mathematical Statistics
- external identifiers
-
- scopus:84958693876
- ISSN
- 1050-5164
- DOI
- 10.1214/15-AAP1097
- language
- English
- LU publication?
- no
- id
- f9948ed9-92ca-416b-ad35-fca5e3915ca5
- date added to LUP
- 2017-09-01 11:55:16
- date last changed
- 2022-04-09 18:41:29
@article{f9948ed9-92ca-416b-ad35-fca5e3915ca5, abstract = {{In this paper, we shall be concerned with geometric functionals and excursion probabilities for some nonlinear transforms evaluated on Fourier components of spherical random fields. In particular, we consider both random spherical harmonics and their smoothed averages, which can be viewed as random wavelet coefficients in the continuous case. For such fields, we consider smoothed polynomial transforms; we focus on the geometry of their excursion sets, and we study their asymptotic behaviour, in the high-frequency sense. We focus on the analysis of Euler–Poincaré characteristics, which can be exploited to derive extremely accurate estimates for excursion probabilities. The present analysis is motivated by the investigation of asymmetries and anisotropies in cosmological data. The statistics we focus on are also suitable to deal with spherical random fields which can only be partially observed, the canonical example being provided by the masking effect of the Milky Way on Cosmic Microwave Background (CMB) radiation data.<br/><br/>}}, author = {{Vadlamani, Sreekar and Marinucci, Domenico}}, issn = {{1050-5164}}, keywords = {{high-frequency asymptotics; spherical random fields; Minkowski functionals; excursion sets; Gaussian subordination; 60G60; 62M15; 53C65; 42C15}}, language = {{eng}}, number = {{1}}, pages = {{462--506}}, publisher = {{Institute of Mathematical Statistics}}, series = {{Annals of Applied Probability}}, title = {{High-frequency asymptotics for Lipschitz–Killing curvatures of excursion sets on the sphere}}, url = {{http://dx.doi.org/10.1214/15-AAP1097}}, doi = {{10.1214/15-AAP1097}}, volume = {{26}}, year = {{2016}}, }