V.A. Malyshev
Probability around the Quantum Gravity. Part 1: Planar Pure Gravity.
(483K, Postscript)
ABSTRACT. In this paper we study stochastic dynamics which leaves quantum
gravity equilibrium distribution invariant. We start theoretical study of this dynamics (earlier it
was only used for Monte-Carlo simulation). Main new results concern the
existence and properties of local correlation functions in the thermodynamic limit.
The study of dynamics constitutes a third part of the series of
papers where more general class of processes
were studied (but it is self-contained), those processes have
some universal significance
in probability and
they cover most concrete processes, also they have many examples in computer
science and biology. At the same time the paper can serve an introduction to quantum gravity for a probabilist:
we give a rigorous
exposition of quantum gravity in the planar pure gravity case. Mostly
we use combinatorial techniques, instead of more popular in physics random
matrix models, the central point is the famous $\alpha =-\frac{7}{2}$ exponent.