Probability Seminar

Title: Multiple Equilibria and Resilience in Large Complex Systems: beyond May-Wigner model.
Speaker: Yan Fyodorov
Speaker Info: Kings College
Brief Description:
Special Note:

I will discuss two different models of randomly coupled N>>1 autonomous differential equations with the aim of counting their fixed points (aka equilibria), and classifying them by their ''instability index'', i.e. the number of unstable directions. In the first model ( studied in a joint paper with G. Ben Arous & B. Khoruzhenko) characterized by both translational and rotational statistical symmetry of the vector field, we estimate the probability of an equilibrium to have a given index in a phase with exponentially many equilibria. In the second model (studied with S. Belga Fedeli & J. Ipsen) characterized by only rotational statistical symmetry around a chosen stable equilibrium, we find a characteristic distance beyond which the multitude of equilibria prevents a trajectory to go towards the stable equilibrium. This may help to shed some light on ''resilience'' mechanisms of complex ecosystems.
Date: Wednesday, April 14, 2021
Time: 9:00am
Where: https://northwestern.zoom.us/j/907400031
Contact Person: Antonio Auffinger
Contact email: tuca@northwestern.edu
Contact Phone:
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