CRITICAL SCALING IN THE MATRIX MODEL ON A BETHE TREE

The matrix model with a Bethe tree embedding space (coincides at large N with the Kazakov-Migdal ''induced QCD'' model1) is investigated. We further elaborate the Riemann-Hibert approach of Ref. 2 assuming certain holomorphic properties of the solution. The critical scaling (an edge singularity of the density) is found to be gamma(str) = - 1/pi arccos D, for \D\ <1, gamma(str) = - 1/pi arccos D/2D-1, for D > 1. Explicit solutions are constructed at D = 1/2 and D = infinity.