EconPapers    
Economics at your fingertips  
 

A note on the reduction principle for the nodal length of planar random waves

Anna Vidotto

Statistics & Probability Letters, 2021, vol. 174, issue C

Abstract: Inspired by Marinucci et al. (2020), we prove that the nodal length of a planar random wave BE, i.e. the length of its zero set BE−1(0), is asymptotically equivalent, in the L2-sense and in the high-frequency limit E→∞, to the integral of H4(BE(x)), H4 being the fourth Hermite polynomial. As straightforward consequences, we obtain Moderate Deviation estimates and a central limit theorem in Wasserstein distance. This complements recent findings by Nourdin et al. (2019) and Peccati and Vidotto (2020).

Keywords: Nodal length; Random plane waves; Sample trispectrum; Berry’s cancellation; Quantitative central limit theorem (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: Track citations by RSS feed

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0167715221000523
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:stapro:v:174:y:2021:i:c:s0167715221000523

Ordering information: This journal article can be ordered from
http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

DOI: 10.1016/j.spl.2021.109090

Access Statistics for this article

Statistics & Probability Letters is currently edited by Somnath Datta and Hira L. Koul

More articles in Statistics & Probability Letters from Elsevier
Bibliographic data for series maintained by Catherine Liu ().

 
Page updated 2021-07-10
Handle: RePEc:eee:stapro:v:174:y:2021:i:c:s0167715221000523