Rigidity of the 3D hierarchical Coulomb gas
Geometric functional analysis and applications November 13, 2017 - November 17, 2017
Location: MSRI: Simons Auditorium
60K35 - Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
82B05 - Classical equilibrium statistical mechanics (general)
The mathematical analysis of Coulomb gases, especially in dimensions higher than one, has been the focus of much recent activity. For the 3D Coulomb, there is a famous prediction of Jancovici, Lebowitz and Manificat that if N is the number of particles falling in a given region, then N has fluctuations of order cube-root of E(N). I will talk about the recent proof of this conjecture for a closely related model, known as the 3D hierarchical Coulomb gas. I will also try to explain, through some toy examples, why such unusually small fluctuations may be expected to appear in interacting gases
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