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Seminar

Random Determinants, the Elastic Manifold, and Landscape Complexity Beyond Invariance September 03, 2021 (11:00 AM PDT - 12:00 PM PDT)
Parent Program:
Location: MSRI: Online/Virtual, Simons Auditorium
Speaker(s) Benjamin McKenna (New York University, Courant Institute)
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Random Determinants, The Elastic Manifold, And Landscape Complexity Beyond Invariance

Abstract/Media

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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.

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