Central limit theorems; Functional convergence; Gaussian fields; Nodal sets; Random waves; Total disorder; Statistical and Nonlinear Physics; Mathematical Physics
Abstract :
[en] We consider Berry’s random planar wave model (J Phys A 10(12):2083–2092, 1977), and prove spatial functional limit theorems—in the high-energy limit—for discretized and truncated versions of the random field obtained by restricting its nodal length to rectangular domains. Our analysis is crucially based on a detailed study of the projection of nodal lengths onto the so-called second Wiener chaos, whose high-energy fluctuations are given by a Gaussian total disorder field indexed by polygonal curves. Such an exact characterization is then combined with moment estimates for suprema of stationary Gaussian random fields, and with a tightness criterion by Davydov and Zitikis (Ann Inst Stat Math 60(2):345–365, 2008).
Disciplines :
Mathematics
Author, co-author :
Notarnicola, Massimo; Department of Mathematics, University of Luxembourg, Esch-sur-Alzette, Luxembourg
PECCATI, Giovanni ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH)
Vidotto, Anna; Department of Mathematics and Applications, University of Naples Federico II, Naples, Italy
External co-authors :
yes
Language :
English
Title :
Functional Convergence of Berry’s Nodal Lengths: Approximate Tightness and Total Disorder
Giovanni Peccati is partially supported by the FNR Grant HDSA (O21/16236290/HDSA) at Luxembourg University. Anna Vidotto is supported by the co-financing of the European Union—FSE-REACT-EU, PON Research and Innovation 2014-2020, DM 1062/2021.
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