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A note on global suprema of band-limited spherical random functions

Vadlamani, Sreekar LU and Marinucci, Domenico (2015) In Statistics and Probability Letters 96. p.141-148
Abstract
In this note, we investigate the behaviour of suprema for band-limited spherical random fields. We prove upper and lower bound for the expected values of these suprema, by means of metric entropy arguments and discrete approximations; we then exploit the Borell–TIS inequality to establish almost sure upper and lower bounds for their fluctuations. Band limited functions can be viewed as restrictions on the sphere of random polynomials with increasing degrees, and our results show that fluctuations scale as the square root of the logarithm of these degrees.
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author
publishing date
type
Contribution to journal
publication status
published
subject
keywords
spherical random fields, suprema, metric entropy, 60G60, 62M15, 53C65, 42C15, almost sure convergence
in
Statistics and Probability Letters
volume
96
pages
8 pages
publisher
Elsevier
external identifiers
  • scopus:84908347955
ISSN
0167-7152
DOI
10.1016/j.spl.2014.09.018
language
English
LU publication?
no
id
2cf91045-1fcd-4ffe-8730-ec84eb87a613
date added to LUP
2017-09-01 11:58:26
date last changed
2017-09-03 05:26:41
@article{2cf91045-1fcd-4ffe-8730-ec84eb87a613,
  abstract     = {In this note, we investigate the behaviour of suprema for band-limited spherical random fields. We prove upper and lower bound for the expected values of these suprema, by means of metric entropy arguments and discrete approximations; we then exploit the Borell–TIS inequality to establish almost sure upper and lower bounds for their fluctuations. Band limited functions can be viewed as restrictions on the sphere of random polynomials with increasing degrees, and our results show that fluctuations scale as the square root of the logarithm of these degrees.},
  author       = {Vadlamani, Sreekar and Marinucci, Domenico},
  issn         = {0167-7152},
  keyword      = {spherical random fields,suprema,metric entropy,60G60,62M15,53C65,42C15,almost sure convergence},
  language     = {eng},
  pages        = {141--148},
  publisher    = {Elsevier},
  series       = {Statistics and Probability Letters},
  title        = {A note on global suprema of band-limited spherical random functions},
  url          = {http://dx.doi.org/10.1016/j.spl.2014.09.018},
  volume       = {96},
  year         = {2015},
}