Séminaire Orléans

Periods of eigenfunction clusters: a probabilistic approach.
Suresh Eswarathasan
Thursday 28 November 2013 14:00 -  Orléans -  Salle de Séminaire

Résumé :
Let M be a compact surface with its set of periodic geodesics in the cotangent bundle having Liouville measure zero. Using an asymptotic proved by S. Zelditch involving the Kuznecov trace formula, we utilize an idea of Burq and Lebeau to study random linear combination $u$ of Laplace-Beltrami eigenfunctions in the spectral window $[\lambda, \lambda + 1).$. These results are a contrast to the deterministic bounds obtained by Chen-Sogge, Reznikov, and Zelditch. If time permits, we will also present probabilistic versions of $L^p$ restriction bounds along submanifolds. Furthermore, our results hold under more general assumptions.

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