We describe protein–protein recognition within the frame of the random energy model of statistical physics. We simulate, by docking the component proteins, the process of association of two proteins that form a complex. We obtain the energy spectrum of a set of protein–protein complexes of known three-dimensional structure by performing docking in random orientations and scoring the models thus generated. We use a coarse protein representation where each amino acid residue is replaced by its Voronoï cell, and derive a scoring function by applying the evolutionary learning program ROGER to a set of parameters measured on that representation. Taking the scores of the docking models to be interaction energies, we obtain energy spectra for the complexes and fit them to a Gaussian distribution, from which we derive physical parameters such as a glass transition temperature and a specificity transition temperature.