A Phase Diagram for Langevin Dynamics of p-Spin Glasses

Topic: 
A Phase Diagram for Langevin Dynamics of p-Spin Glasses
Date & Time: 
Tuesday, March 13, 2018 -
14:00 to 15:00
Speaker: 
Reza Gheissari, New York University
Location: 
Room 264, Geography Building, 3663 Zhongshan Road North, Shanghai

Abstract:
Consider a random polynomial H of degree p on the sphere in dimension N: when the coefficients are i.i.d. Gaussian, this is the spherical p-spin glass. This Hamiltonian H has exponentially many in N critical points of every index; moreover, its Langevin dynamics at low temperature are known to take exponentially long in N to equilibrate and are believed to exhibit aging on shorter timescales.

We prove an approximate phase diagram for (H(Xt),|∇ H(Xt)|2) on order-one time scales. We will discuss consequences of this phase diagram, e.g., uniformly over all starting states, Langevin dynamics at any temperature reaches and remains in a region of macroscopically negative energies, and is repelled by macroscopic neighborhoods of critical points.

This is a Joint work with G. Ben Arous and A. Jagannath.

Biography:
Reza Gheissari is a 4th year Ph.D. student at NYU Courant co-advised by Charles Newman and Eyal Lubetzky. His research interests are in probability theory and mathematical physics, including dynamics of spin systems, their phase transitions and mixing times.

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Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai

Location & Details: 

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