Nodal length fluctuations for arithmetic random waves

20 October 2011
Igor Wigman
<p>Using the spectral multiplicities of the standard torus, we<br />endow the Laplace eigenspaces with Gaussian probability measures.<br />This induces a notion of random Gaussian eigenfunctions<br />on the torus ("arithmetic random waves''.) &nbsp;We study the<br />distribution of&nbsp;the nodal length of random Laplace eigenfunctions for high<br />eigenvalues,and our primary result is that the asymptotics for the variance is<br />non-universal, and is intimately related to the arithmetic of<br />lattice points lying on a circle with radius corresponding to the <br />energy. This work is joint with Manjunath Krishnapur and Par Kurlberg<br /><br /></p>
  • Number Theory Seminar