In this paper, we prove absence of temperature chaos for the two-dimensional discrete Gaussian free field using convergence full extremal process, which has been obtained recently by Biskup and Louidor. This means that overlap two points chosen under Gibbs measures at different temperatures a nontrivial distribution. Whereas distribution is same as random energy model when are sampled temperatu...

We study the overlap distribution of two particles chosen under Gibbs measure at temperatures for branching Brownian motion. first prove convergence using extended extremal process obtained by Bovier and Hartung [8]. then that mean points different is strictly smaller than in Derrida’s random energy model. The proof this last result achieved with description decoration point Aïdékon, Berestycki...