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Section: New Results

DLR equations and rigidity for the Sine-$\beta$ process

The work [20] by A. Hardy and his collaborators, recently accepted for publication in Communications on Pure and Applied Mathematics, provides a “statistical physics” description of the sine-$\beta$ process by means of Dobroshin-Lanford-Ruelle (DLR) equations. This basically allows to give a meaning to “the natural infinite configurations process on the real line in the 2D Coulomb interaction”, provided there is a unique solution to the DLR equation which turns out to be true in this setting.