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UID:20250712T200504EDT-5507gwcub1@132.216.98.100
DTSTAMP:20250713T000504Z
DESCRIPTION:Title: Relative Instability and Concentration of Equilibria in 
 Non-Gradient Dynamics.\n\nAbstract. A classical picture in the theory of c
 omplex high-dimensional random functions is that the gradient dynamics of 
 the function may become slowed and trapped by an abundance of saddles and 
 sinks in the energy landscape. Specifically\, when a model has an exponent
 ially large number of such points\, the dynamics are expected to be slow a
 nd 'glassy'\, a belief now confirmed in a variety of models.\n\nIn non-gra
 dient dynamics however\, another phase is possible. In particular\, work o
 f Ben Arous\, Fyodorov\, and Khorozhenko on the generalized May-Wigner mod
 el found evidence that if the strength of the non-gradient terms were brou
 ght past a certain threshold\, the total number of equilibria (stationary 
 points) would remain exponentially large\, while the number of stable equi
 libria would go from being exponentially large\, to simply vanishing entir
 ely. These two regimes were coined as relative and absolute instability\, 
 respectively\, and have since been predicted to occur in a variety of mode
 ls.\n\nWe rigorously confirm this picture in the non-gradient analog for t
 he spherical p-spin model.\n\nTo do so\, we demonstrate concentration of t
 he 'annealed' complexity (exponential order) of stable and general equilib
 ria\, recently computed by Fyodorov and Garcia\, around their typical valu
 es\, mirroring recent work of Subag and Zeitouni in the relaxational case.
  The key input is a new computation for the higher moments of the characte
 ristic polynomials of matrices sampled from the elliptic ensemble\, as wel
 l as general extensions of the recent framework of Ben Arous\, Bourgade\, 
 and McKenna to the non-relaxational case.\n\n \n\nZoom link: https://mcgil
 l.zoom.us/j/89737173009?pwd=UzlwZkVPK0RnYXk4VGM2aXo4V3Q2QT09\n
DTSTART:20230330T153000Z
DTEND:20230330T163000Z
LOCATION:Room 1214\, Burnside Hall\, CA\, QC\, Montreal\, H3A 0B9\, 805 rue
  Sherbrooke Ouest
SUMMARY:Pax Kivimae (Northwestern University)
URL:/mathstat/channels/event/pax-kivimae-northwestern-
 university-347401
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