Gaussian complex zeros: conditional distribution on rare events

Abstract: The zero process of the Gaussian Entire Function is a natural example of a two-dimensional random point configuration whose distribution is invariant under rigid motions of the plane. Another well-studied example is the infinite Ginibre ensemble. Due to non-trivial correlations, the features of these two processes are quite different from the ones of the homogeneous Poisson point process. For this reason, these processes are of interest to analysts, probabilists, and mathematical physicists.

Some particularly interesting statistical phenomena to study are rare events, when the number of points in a certain large domain is very different from its expected value. An important example is the ‘hole event’, when there are no points at all. For the Ginibre ensemble, the hole event can be studied using some classical tools from potential theory. This is no longer true for complex zeros, and in this talk I will mention some of the challenges and describe new results.

Based on joint works with S. Ghosh (NUS) and A. Wennman (Tel Aviv)

probability

Audience: advanced learners

Bangalore Probability Seminar

Series comments: The link to zoom meeting can be found on the seminar's google calendar - www.isibang.ac.in/~d.yogesh/BPS.html