[Ml-stat-talks] Gérard Ben Arous in tomorrow's colloquium at ORFE
Philippe Rigollet
rigollet at Princeton.EDU
Mon Nov 19 09:42:27 EST 2012
=== ORFE Colloquium Announcement ===
DATE: Tuesday, November 20, 2012
TIME: 4:30pm
LOCATION: Room 101, Sherrerd Hall
SPEAKER: Gérard Ben Arous. Courant Institute of Mathematical Sciences, NYU
TITLE: Complexity of Random Smooth Functions of Many Variables
ABSTRACT: Can one count the number of critical points for random smooth functions of many variables?
How complex is a typical random smooth function?
How complex is the topology of its level sets?
We study here the simplest case of smooth Gaussian random functions defined on the sphere
in high dimensions. We show that such a randomly chosen smooth function is very complex,
i.e. that it’s number of critical points of given index is exponentially large. We also study the
topology of the level sets of these functions, and give sharp estimates of their Euler
characteristic. This study, which is a joint work with Tuca Auffinger (Chicago) and partly
with Jiri Cerny (Vienna), relies rather surprisingly on Large deviations results in Random
Matrix Theory.
The main motivation comes from the study of energy landscapes for general spherical spinglasses. Time-permitting, I will detail the interesting picture we get for the complexity of
these random Hamiltonians.
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