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Universality principles for random polynomials

Banff International Research Station for Mathematical Innovation and Discovery

In this talk, I will present several universality principles concerned with zero distribution of random polynomials or more generally random holomorphic sections of high powers $L^{\otimes n}$ of positive line bundle $L\to X$ defined over a projective manifold endowed with a continuous metric. In one direction, universality phenomenon indicates that under natural assumptions, asymptotic distribution of (appropriately normalized) zeros of random polynomials is independent of the choice of probability law defined on random polynomials. Another form of universality is asymptotic normality of smooth linear statistics of zero currents. Finally, if time permits, I will also describe some recent results on universality of scaling limits of correlations between simultaneous zeros of random polynomials.

Mathematics; Several complex variables and analytic spaces; Potential theory; Global analysis

video/mp4

Author affiliation: Syracuse University

2017-10-13

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/63279

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/