Peeling Random Planar Maps (Paperback)

Nicolas Curien

ISBN 10: 3031368533 / ISBN 13: 9783031368530

Published by Springer International Publishing AG, Cham, 2023

About this Item

Paperback. 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 Ecole d'Ete de Probabilites 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. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.

Seller Inventory # 9783031368530

Bibliographic Details

• Title: Peeling Random Planar Maps (Paperback)
• Publisher: Springer International Publishing AG, Cham
• Publication Date: 2023
• Language: English
• ISBN 10: 3031368533
• ISBN 13: 9783031368530
• Binding: Paperback
• Edition: 1st Edition
• Condition: new

About this title

Synopsis

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.

About the Author

Nicolas Curien has been a Professor at Université Paris-Saclay since 2014. He works on random geometry in a broad sense.