211 citations · 1.3k across the 126 of their papers we have counts for
7 papers · 1 filter
Critical values of random analytic functions on complex manifolds
Renjie Feng, Steve Zelditch
We study the asymptotic distribution of critical values of random holomorphic `polynomials' s_n on a Kaehler manifold M as the degree n tends to infinity. By `polynomial' of degree…
Random orthonormal bases of spaces of high dimension
Steve Zelditch
We consider a sequence H_N of Hilbert spaces of dimensions d_N tending to infinity. The motivating examples are eigenspaces or quasi-mode spaces of a Laplace or Schrodinger operato…
Ergodicity and intersections of nodal sets and geodesics on real analytic surfaces
Steve Zelditch
We consider the the intersections of the complex nodal set of the analytic continuation of an eigenfunction of the Laplacian on a real analytic surface with the complexification of…
Lower bounds on the Hausdorff measure of nodal sets II
Christopher D. Sogge, Steve Zelditch
We give a very short argument showing how the main identity from our earlier paper (Sogge and Zelditch, 2011) immediately leads to the best lower bound currently known (Colding and…
The Cauchy problem for the homogeneous Monge-Ampere equation, III. Lifespan
Yanir A. Rubinstein, Steve Zelditch
We prove several results on the lifespan, regularity, and uniqueness of solutions of the Cauchy problem for the homogeneous complex and real Monge-Ampere equations (HCMA/HRMA) unde…
Eigenfunctions and Nodal Sets
S. Zelditch
This is a survey of recent results on eigenfunctions of the Laplacian on compact Riemannian manifolds and their nodal sets. It is the write-up of my talk at JDG 2011.