271 citations · 947 across the 35 of their papers we have counts for
36 papers
Stochastic Kähler geometry: from random zeros to random metrics
Bernard Shiffman, Steve Zelditch
We provide a survey of results on the statistics of random sections of holomorphic line bundles on Kähler manifolds, with an emphasis on the resulting asymptotics when a line bundl…
Closed-Form Parametric Equation for the Minkowski Sum of Ellipsoids in and Associated Volume Bounds
Gregory S. Chirikjian, Bernard Shiffman
General results on convex bodies are reviewed and used to derive an exact closed-form parametric formula for the Minkowski sum boundary of arbitrary ellipsoids in -dimension…
Asymptotic expansion of the variance of random zeros on complex manifolds
Bernard Shiffman
Linear statistics of random zero sets are integrals of smooth differential forms over the zero set and as such are smooth analogues of the volume of the random zero set inside a fi…
Uniformly bounded orthonormal sections of positive line bundles on complex manifolds
Bernard Shiffman
We show the existence of uniformly bounded sequences of increasing numbers of orthonormal sections of powers of a positive holomorphic line bundle on a compact Kähler man…
Asymptotic expansion of the off-diagonal Bergman kernel on compact Kähler manifolds
Zhiqin Lu, Bernard Shiffman
We compute the first four coefficients of the asymptotic off-diagonal expansion of the Bergman kernel for the N-th power of a positive line bundle on a compact Kaehler manifold, an…
Random complex fewnomials, I
Bernard Shiffman, Steve Zelditch
We introduce several notions of `random fewnomials', i.e. random polynomials with a fixed number f of monomials of degree N. The f exponents are chosen at random and then the coeff…