Seminar

Random Determinants, the Elastic Manifold, and Landscape Complexity Beyond Invariance

September 03, 2021 (11:00 AM PDT - 12:00 PM PDT)

Parent Program:	Universality and Integrability in Random Matrix Theory and Interacting Particle Systems
Location:	SLMath: Online/Virtual, Eisenbud Auditorium

Speaker(s)

Benjamin McKenna (New York University, Courant Institute)

Description

No Description

Keywords and Mathematics Subject Classification (MSC)

Primary Mathematics Subject Classification No Primary AMS MSC

Secondary Mathematics Subject Classification No Secondary AMS MSC

Video

Random Determinants, The Elastic Manifold, And Landscape Complexity Beyond Invariance

Abstract/Media

To participate in this seminar, please register HERE.

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.

No Notes/Supplements Uploaded

Random Determinants, The Elastic Manifold, And Landscape Complexity Beyond Invariance