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.
KRATZ, M. and PICCO, P. (2004). On a representation of Gibbs measure for R.E.M. Annals of Applied Probability, 14(2), pp. 651-677.