Planar Maps, Random Walks and Circle Packing

• - Introduction. - Random Walks and Electric Networks. - The Circle Packing Theorem. - Parabolic and Hyperbolic Packings. - Planar Local Graph Limits. - Recurrence of Random Planar Maps. - Uniform Spanning Trees of Planar Graphs. - Related Topics.

“The most remarkable aspect of the Lecture Notes is the reader-friendly structure and the style in which it has been written. There are masses of examples either worked out in the text or left for the reader. A number of facts are equipped with graphical illustrations. The importance of this Lecture Notes by the author both from the practical and from the theoretical standpoint is unquestionable.” (Viktor Ohanyan, zbMATH 1471.60007, 2021)“The whole material is very nicely presented and the book may serve as the support for a graduate course in probability.” (Nicolas Curien, Mathematical Reviews, November, 2020)