Asymptotics of polynomials and eigenfunctions
نویسنده
چکیده
We review some recent results on asymptotic properties of polynomials of large degree, of general holomorphic sections of high powers of positive line bundles over Kähler manifolds, and of Laplace eigenfunctions of large eigenvalue on compact Riemannian manifolds. We describe statistical patterns in the zeros, critical points and Lp norms of random polynomials and holomorphic sections, and the influence of the Newton polytope on these patterns. For eigenfunctions, we discuss Lp norms and mass concentration of individual eigenfunctions and their relation to dynamics of the geodesic flow. 2000 Mathematics Subject Classification: 35P20, 30C15, 32A25, 58J40, 60D05, 81S10, 14M25.
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