These Lecture Notes provide an introduction to the study of those discrete surfaces which are obtained by randomly gluing polygons along their sides in a plane. The focus is on the geometry of such random planar maps (diameter, volume growth, scaling and local limits...) as well as the behavior of statistical mechanics models on them (percolation, simple random walks, self-avoiding random walks...).
A "Markovian" approach is adopted to explore these random discrete surfaces, which is then related to the analogous one-dimensional random walk processes. This technique, known as "peeling exploration" in the literature, can be seen as a generalization of the well-known coding processes for random trees (e.g. breadth first or depth first search). It is revealed that different types of Markovian explorations can yield different types of information about a surface.
Based on an École d'Été de Probabilités de Saint-Flour course delivered by the author in 2019, the book is aimed at PhD students and researchers interested in graph theory, combinatorial probability and geometry. Featuring open problems and a wealth of interesting figures, it is the first book to be published on the theory of random planar maps.| ISBN: | 9783031368530 |
| Publication date: | 21st November 2023 |
| Author: | Nicolas Curien |
| Publisher: | Springer an imprint of Springer Nature Switzerland |
| Format: | Paperback |
| Pagination: | 240 pages |
| Series: | Lecture Notes in Mathematics |
| Genres: |
Probability and statistics Stochastics Geometry Combinatorics and graph theory |
These Lecture Notes provide an introduction to the study of those discrete surfaces which are obtained by randomly gluing polygons along their sides in a plane. The focus is on the geometry of such random planar maps (diameter, volume growth, scaling and local limits...) as well as the behavior of statistical mechanics models on them (percolation, simple random walks, self-avoiding random walks...).A "Markovian" approach is adopted to explore these random discrete surfaces, which is then related to the analogous one-dimensional random walk processes.
Peeling Random Planar Maps features in the following genres: Probability and statistics, Stochastics, Geometry, Combinatorics and graph theory
Paperback. £49.49, down from the £54.99 cover price. Not Available.
Peeling Random Planar Maps was written by Nicolas Curien and published by Springer an imprint of Springer Nature Switzerland
Peeling Random Planar Maps has 240 pages
Yes it is part of Lecture Notes in Mathematics series
£49.49, reduced from £54.99. Not Available.