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Abstract
There is a close connection between the ground state of noninteracting fermions in a box with classical (absorbing, reflecting, and periodic) boundary conditions and the eigenvalue statistics of the classical compact groups. The associated determinantal point processes can be extended in two natural directions: (i) we consider the full family of admissible quantum boundary conditions (i.e., selfadjoint extensions) for the Laplacian on a bounded interval, and the corresponding projection correlation kernels; (ii) we construct the grand canonical extensions at finite temperature of the projection kernels, interpolating from Poisson to random matrix eigenvalue statistics. The scaling limits in the bulk and at the edges are studied in a unified framework, and the question of universality is addressed. Whether the finite temperature determinantal processes correspond to the eigenvalue statistics of some matrix models is, a priori, not obvious. We complete the picture by constructing a finite temperature extension of the Haar measure on the classical compact groups. The eigenvalue statistics of the resulting grand canonical matrix models (of random size) corresponds exactly to the grand canonical measure of free fermions with classical boundary conditions.
Original language  English 

Pages (fromto)  768801 
Number of pages  34 
Journal  Journal of Statistical Physics 
Volume  171 
Issue number  5 
Early online date  20 Apr 2018 
DOIs  
Publication status  Published  Jun 2018 
Keywords
 Determinantal processes
 Group heat kernel
 Noninteracting fermions
 Nonintersecting paths
 Quantum boundary conditions
 Random matrix theory and extensions
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Professor Francesco Mezzadri
 Probability, Analysis and Dynamics
 School of Mathematics  Professor of Mathematical Physics
 Applied Mathematics
 Mathematical Physics
Person: Academic , Member