scholarly journals Nodal area distribution for arithmetic random waves

2019 ◽  
Vol 372 (5) ◽  
pp. 3539-3564 ◽  
Author(s):  
Valentina Cammarota
Keyword(s):  
Random Waves ◽  
Area Distribution ◽  
Arithmetic Random Waves

scholarly journals Boundary Effect on the Nodal Length for Arithmetic Random Waves, and Spectral Semi-correlations

2020 ◽  
Vol 376 (2) ◽  
pp. 1261-1310 ◽  
Author(s):  
Valentina Cammarota ◽  
Oleksiy Klurman ◽  
Igor Wigman
Keyword(s):  
Boundary Effect ◽  
Random Waves ◽  
Arithmetic Random Waves

scholarly journals Non-Universality of Nodal Length Distribution for Arithmetic Random Waves

2016 ◽  
Vol 26 (3) ◽  
pp. 926-960 ◽  
Author(s):  
Domenico Marinucci ◽  
Giovanni Peccati ◽  
Maurizia Rossi ◽  
Igor Wigman
Keyword(s):  
Length Distribution ◽  
Random Waves ◽  
Arithmetic Random Waves

scholarly journals Asymptotic distribution of nodal intersections for arithmetic random waves

Nonlinearity ◽  
2018 ◽  
Vol 31 (10) ◽  
pp. 4472-4516 ◽  
Author(s):  
Maurizia Rossi ◽  
Igor Wigman
Keyword(s):  
Asymptotic Distribution ◽  
Random Waves ◽  
Arithmetic Random Waves

scholarly journals On the variance of the nodal volume of arithmetic random waves

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Giacomo Cherubini ◽  
Niko Laaksonen
Keyword(s):  
Upper Bound ◽  
Power Saving ◽  
Current Method ◽  
Random Waves ◽  
Dimensional Torus ◽  
Nodal Set ◽  
Arithmetic Random Waves

Abstract Rudnick and Wigman (2008) conjectured that the variance of the volume of the nodal set of arithmetic random waves on the d-dimensional torus is O ⁢ ( E / 𝒩 ) {O(E/\mathcal{N})} , as E → ∞ {E\to\infty} , where E is the energy and 𝒩 {\mathcal{N}} is the dimension of the eigenspace corresponding to E. Previous results have established this with stronger asymptotics when d = 2 {d=2} and d = 3 {d=3} . In this brief note we prove an upper bound of the form O ⁢ ( E / 𝒩 1 + α ⁢ ( d ) - ϵ ) {O(E/\mathcal{N}^{1+\alpha(d)-\epsilon})} , for any ϵ > 0 {\epsilon>0} and d ≥ 4 {d\geq 4} , where α ⁢ ( d ) {\alpha(d)} is positive and tends to zero with d. The power saving is the best possible with the current method (up to ϵ) when d ≥ 5 {d\geq 5} due to the proof of the ℓ 2 {\ell^{2}} -decoupling conjecture by Bourgain and Demeter.

scholarly journals Nodal length fluctuations for arithmetic random waves

2013 ◽  
Vol 177 (2) ◽  
pp. 699-737 ◽  
Author(s):  
Manjunath Krishnapur ◽  
Pär Kurlberg ◽  
Igor Wigman
Keyword(s):  
Random Waves ◽  
Arithmetic Random Waves

scholarly journals The defect of toral Laplace eigenfunctions and arithmetic random waves

Nonlinearity ◽  
2021 ◽  
Vol 34 (9) ◽  
pp. 6651-6684
Author(s):  
Pär Kurlberg ◽  
Igor Wigman ◽  
Nadav Yesha
Keyword(s):  
Random Waves ◽  
Arithmetic Random Waves
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