MaxWeight scheduling in a generalized switch: State space collapse and workload minimization in heavy traffic

In this work we consider a problem related to the equilibrium Statistical Mechanics of Spin Glasses, namely the study of the Gibbs measure of the Random Energy Model. For solving this problem new results of independent interest on sums of spacings for i.i.d. Gaussian random variables are presented. Then we give a precise description of the support of the Gibbs measure below the critical temperature.

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