Work

Correlation structure and resonant pairs for arithmetic random waves

Year: 2024

Type: article

Abstract: The geometry of Arithmetic Random Waves has been extensively investigated in the last fifteen years, starting from the seminal papers (Rudnick and Wigman, 2008; Oravecz et al., 2008). In this paper we study the correlation structure among different functionals such as nodal length, boundary length of excursion sets, and the number of intersection of nodal sets with deterministic curves in different classes; the amount of correlation depends in a subtle fashion from the values of the thresholds considered and the symmetry properties of the deterministic curves. In particular, we prove the existence of resonant pairs of threshold values where the asymptotic correlation is full, that is, at such values one functional can be perfectly predicted from the other in the high energy limit. We focus mainly on the 2-dimensional case but we discuss some specific extensions to dimension 3.

Source: Stochastic Processes and their Applications

DOI: 10.1016/j.spa.2024.104525

Authors: Valentina Cammarota, Riccardo W. Maffucci, Domenico Marinucci, Maurizia Rossi

Institutions: Sapienza University of Rome, University of Turin, University of Rome Tor Vergata, University of Milano-Bicocca

Language: English

Topic: Analytic Number Theory Research

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,420

Funders: Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung, Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni