Planar Maps, Random Walks and Circle Packing

A planar map is a graph that can be drawn in the plane without crossing edges, together with a specification of the cyclic ordering of the edges incident to each vertex.

This open access book focuses on the interplay between Random Walks on planar maps and Koebe’s circle packing theorem. Entirely self-contained and aimed to fully accompany a single-semester graduate course. Many classical proofs have been simplified and streamlined. Contains numerous useful exercises.