About this book
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. One widely applicable method of drawing planar graphs is given by Koebe’s circle packing theorem (1936). Various geometric properties of these drawings, such as existence of accumulation points and bounds on the radii, encode important probabilistic information, such as the recurrence/transience of simple random walks and connectivity of the uniform spanning forest. This deep connection is especially fruitful to the study of random planar maps.
The book is aimed at researchers and graduate students in mathematics and is suitable for a single-semester course; only a basic knowledge of graduate level probability theory is assumed.
- DOI https://doi.org/10.1007/978-3-030-27968-4
- Copyright Information The Editor(s) (if applicable) and The Author(s) 2020
- License CC BY
- Publisher Name Springer, Cham
- eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
- Print ISBN 978-3-030-27967-7
- Online ISBN 978-3-030-27968-4
- Series Print ISSN 0075-8434
- Series Online ISSN 1617-9692
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