Yaiza CANZANI GARCIA - Statistics of randomized Laplace eigenfunctions
Channel: Institut des Hautes Études Scientifiques (IHÉS)
Date: 2017-12-27

There  are  several  questions  about  the  behavior  of  Laplace  eigenfunctions  that  are extremely hard to tackle and hence remain unsolved. Among the features that we don’t fully  understand  yet  are:  the  number  of  critical  points,  the  size  of  the  zero  set,  the number  of  components  of  the  zero  set,  and  the  topology  of  such  components.  A natural  approach  is  then  to  randomize  the  problem  and  study  these  features  for  a 
randomized version  of  the  eigenfunctions.  In  this  talk  I  will  present  several  results  that tackle the problems described above for random linear combinations of eigenfunctions (with  Gaussian  coefficients)  on  a  compact  Riemannian  manifold.
This  talk  is  based  on joint works with Boris Hanin and Peter Sarnak.