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Random determinants, the elastic manifold, and landscape complexity beyond invariance

September 23, 2022 @ 11:00 am - 12:00 pm

Member Seminar

Speaker: Ben McKenna

Title: Random determinants, the elastic manifold, and landscape complexity beyond invariance

Abstract: The Kac-Rice formula allows one to study the complexity of high-dimensional Gaussian random functions (meaning asymptotic counts of critical points) via the determinants of large random matrices. We present new results on determinant asymptotics for non-invariant random matrices, and use them to compute the (annealed) complexity for several types of landscapes. We focus especially on the elastic manifold, a classical disordered elastic system studied for example by Fisher (1986) in fixed dimension and by Mézard and Parisi (1992) in the high-dimensional limit. We confirm recent formulas of Fyodorov and Le Doussal (2020) on the model in the Mézard-Parisi setting, identifying the boundary between simple and glassy phases. Joint work with Gérard Ben Arous and Paul Bourgade.

Details

Date:
September 23, 2022
Time:
11:00 am - 12:00 pm
Event Category:

Venue

CMSA Room G10
CMSA, 20 Garden Street
Cambridge, MA 02138 United States
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Phone:
6174967132