Probability related to quantum gravity. Planar gravity

The stochastic dynamics preserving an equilibrium distribution of quantum gravity is considered. This is the first detailed theoretical investigation of this dynamics (earlier it was used for Monte-Carlo simulation). The main result is related to the existence and certain properties of local correlation functions in the thermodynamic limit. At the same time, the paper can serve as a mathematical introduction to quantum gravity because we give a rigorous exposition of quantum gravity in the case of planar pure gravity. We mainly use the combinatorial approach instead of matrix models, which are more popular in physics, and the central point is the famous exponent $\alpha =-\frac72$.