By Jan Ambjørn, Bergfinnur Durhuus, Thordur Jonsson

This graduate point textual content describes in a unified model the statistical mechanics of random walks, random surfaces and random better dimensional manifolds with an emphasis at the geometrical facets of the idea and purposes to the quantization of strings, gravity and topological box conception. With chapters on random walks, random surfaces, two-and higher-dimensional quantum gravity, topological quantum box theories and Monte Carlo simulations of random geometries, the textual content offers a self-contained account of quantum geometry from a statistical box thought viewpoint. The strategy makes use of discrete approximations and develops analytical and numerical instruments. Continuum physics is recovered via scaling limits at part transition issues and the relation to conformal quantum box theories coupled to quantum gravity is defined. an important numerical paintings is roofed, however the major objective is to improve mathematically designated effects that experience huge functions. Many diagrams and references are incorporated.