The partition functions of perturbed ensembles of random regular graphs (RRG) which discretize 2d surfaces and yield perturbed pure 2d quantum gravity will be discussed. The phase transitions for the RRG perturbed by the chemical potentials for short cycles will be demonstrated numerically. The new matrix model for the massive spinless fermions interacting with 2d quantum gravity is found and solved in planar approximation interpolating between c=0 and c=-2 cases. Some aspects of the localization and ergodicity of modes in this model will be clarified.
De Nathan Seiberg
De Vijay Balasubramanian
De Steve Zelditch
De Eva Silverstein
De Eliezer Rabinovici
De Alexander Gorsky
De Rémi Monasson
De David McAllester
De Luca Mazzucato
De Alexander Belavin
De Washington Taylor
De Gérard Ben Arous
