Tel Aviv University, Colloquium Monday, 24/12/2012, 12:15, Schreiber 006 Speaker: Igor Wigman (King's College, London) Title: Nodal length fluctuations for arithmetic random waves. The abstract is given below. Tea and coffee at 12:00, same room. Hope to see you there. For information about future colloquia, see <http://www.math.tau.ac.il/~ostrover/colloquium/colloq2012.html> Yours, Yaron ************************************* Abstract: Using the spectral multiplicities of the standard torus, we endow the Laplace eigenspaces with Gaussian probability measures. This induces a notion of random Gaussian Laplace eigenfunctions on the torus <(â~@~\arithmetic> random <wavesâ~@~]).> We study the distribution of the nodal length of random eigenfunctions for large eigenvalues, and our primary result is that the asymptotics for the variance is non-universal, and is intimately related to the arithmetic of lattice points lying on a circle with radius corresponding to the energy. This work is joint with Manjunath Krishnapur and Par Kurlberg. --------------------------------------------------------- Technion Math Net-2 (TECHMATH2) Editor: Michael Cwikel <techm@math.technion.ac.il> Announcement from: <ostrover@post.tau.ac.il>