2017/09/30 by Turgay Bayraktar, Dan Coman, George Marinescu · 1 citation
Mathematics · #math.CV #math.DG #math.PR #msc:32A60 #msc:60D05 #msc:32L10 #msc:32C20 #msc:32U40 #msc:81Q50
paper · pdf · doi:10.1090/tran/7807
published as Trans. Amer. Math. Soc. 373 (2020), no. 6, 3765-3791 · 28 pages; v.2 is a final update to agree with the published paper. arXiv admin note: text overlap with arXiv:1412.8184
arxiv created 2020/04/13 · arxiv updated 2020/04/15
In this work we prove an universality result regarding the equidistribution of zeros of random holomorphic sections associated to a sequence of singular Hermitian holomorphic line bundles on a compact Kähler complex space X. Namely, under mild moment assumptions, we show that the asymptotic distribution of zeros of random holomorphic sections is independent of the choice of the probability measure on the space of holomorphic sections. In the case when X is a compact Kähler manifold, we also prove an off-diagonal exponential decay estimate for the Bergman kernels of a sequence of positive line bundles on X.