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math.PR2018★ 3 cited
The one-dimensional log-gas free energy has a unique minimiser
Matthias Erbar, Martin Huesmann, Thomas Leblé
We prove that, at every positive temperature, the infinite-volume free energy of the one dimensional log-gas, or beta-ensemble, has a unique minimiser, which is the Sine-beta proce…
math.PR2018
CLT for fluctuations of linear statistics in the Sine-beta process
Thomas Leblé
We prove, for any , a central limit theorem for the fluctuations of linear statistics in the Sine- process, which is the infinite volume limit of the random microscopic beh…
math.PR2018
DLR equations and rigidity for the Sine-beta process
David Dereudre, Adrien Hardy, Thomas Leblé +1
We investigate Sine, the universal point process arising as the thermodynamic limit of the microscopic scale behavior in the bulk of one-dimensional log-gases, or -ensembles…