69 citations · 495 across the 46 of their papers we have counts for
7 papers · 1 filter
On the number of nodal domains of toral eigenfunctions
Jeremiah Buckley, Igor Wigman
We study the number of nodal domains of toral Laplace eigenfunctions. Following Nazarov-Sodin's results for random fields and Bourgain's de-randomisation procedure we establish a p…
Topologies of nodal sets of random band limited functions
Peter Sarnak, Igor Wigman
It is shown that the topologies and nestings of the zero and nodal sets of random (Gaussian) band limited functions have universal laws of distribution. Qualitative features of the…
Fluctuations of the total number of critical points of random spherical harmonics
Valentina Cammarota, Igor Wigman
We determine the asymptotic law for the fluctuations of the total number of critical points of random Gaussian spherical harmonics in the high degree limit. Our results have implic…
Non-Universality of Nodal Length Distribution for Arithmetic Random Waves
Domenico Marinucci, Giovanni Peccati, Maurizia Rossi +1
"Arithmetic random waves" are the Gaussian Laplace eigenfunctions on the two-dimensional torus (Rudnick and Wigman (2008), Krishnapur, Kurlberg and Wigman (2013)). In this paper we…
Fluctuations of the Euler-Poincaré characteristic for random spherical harmonics
Valentina Cammarota, Domenico Marinucci, Igor Wigman
In this short note, we build upon some recent results to present a precise expression for the asymptotic variance of the Euler-Poincaré characteristic for the excursion sets of Gau…
On probability measures arising from lattice points on circles
Par Kurlberg, Igor Wigman
A circle, centered at the origin and with radius chosen so that it has non-empty intersection with the integer lattice , gives rise to a probability measure on the…