TY - JOUR
T1 - Random waves on T3
T2 - Nodal area variance and lattice point correlations
AU - Benatar, Jacques
AU - Maffucci, Riccardo W.
N1 - Publisher Copyright:
© 2017 The Author(s).
PY - 2019/5/17
Y1 - 2019/5/17
N2 - We consider the ensemble of random Gaussian Laplace eigenfunctions on T3 = R3/Z3 ("3 dimensional arithmetic random waves"), and study the distribution of their nodal surface area. The expected area is proportional to the square root of the eigenvalue, or "energy", of the eigenfunction. We show that the nodal area variance obeys an asymptotic law. The resulting asymptotic formula is closely related to the angular distribution and correlations of lattice points lying on spheres.
AB - We consider the ensemble of random Gaussian Laplace eigenfunctions on T3 = R3/Z3 ("3 dimensional arithmetic random waves"), and study the distribution of their nodal surface area. The expected area is proportional to the square root of the eigenvalue, or "energy", of the eigenfunction. We show that the nodal area variance obeys an asymptotic law. The resulting asymptotic formula is closely related to the angular distribution and correlations of lattice points lying on spheres.
UR - http://www.scopus.com/inward/record.url?scp=85068581396&partnerID=8YFLogxK
U2 - 10.1093/imrn/rnx220
DO - 10.1093/imrn/rnx220
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AN - SCOPUS:85068581396
SN - 1073-7928
VL - 2019
SP - 3032
EP - 3075
JO - International Mathematics Research Notices
JF - International Mathematics Research Notices
IS - 10
M1 - rnx220
ER -