Probability Seminar

Title: On the defect ("signed area") of toral Laplace eigenfunctions and exponential sums
Speaker: Igor Wigman
Speaker Info: King's College London
Brief Description:
Special Note:

This talk is based on a joint work with P. Kurlberg and N. Yesha. The defect (also known as "signed area") of a real-valued function defined on a two-dimensional domain is the difference between its positive and negative regions. We are interested in the defect of toral Laplace eigenfunctions (exponential sums) restricted to Planck-scale shrinking subdomains ("shrinking balls"). It is proved that, under a flatness assumption on the exponential sums, the defect asymptotically vanishes on the set of balls centres of almost full measure, for a generic sequence of energy levels. To establish our results we start from Bourgain's de-randomization technique, and also borrow the Integral-Geometric sandwich from Nazarov-Sodin, and also invoke other techniques.
Date: Tuesday, June 02, 2020
Time: 3:00PM
Where: https://northwestern.zoom.us/j/907400031
Contact Person: Julian Gold
Contact email: gold@math.northwestern.edu
Contact Phone:
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