50 Years of First-Passage Percolation
About this Title
Antonio Auffinger, Northwestern University, Evanston, IL, Michael Damron, Georgia Institute of Technology, Atlanta, GA and Jack Hanson, The City College of New York, New York, NY
Publication: University Lecture Series
Publication Year: 2017; Volume 68
ISBNs: 978-1-4704-4183-8 (print); 978-1-4704-4356-6 (online)
MathSciNet review: MR3729447
MSC: Primary 60K35; Secondary 82B43
First-passage percolation (FPP) is a fundamental model in probability theory that has a wide range of applications to other scientific areas (growth and infection in biology, optimization in computer science, disordered media in physics), as well as other areas of mathematics, including analysis and geometry. FPP was introduced in the 1960s as a random metric space. Although it is simple to define, and despite years of work by leading researchers, many of its central problems remain unsolved.
In this book, the authors describe the main results of FPP, with two purposes in mind. First, they give self-contained proofs of seminal results obtained until the 1990s on limit shapes and geodesics. Second, they discuss recent perspectives and directions including (1) tools from metric geometry, (2) applications of concentration of measure, and (3) related growth and competition models. The authors also provide a collection of old and new open questions. This book is intended as a textbook for a graduate course or as a learning tool for researchers.
Graduate students and researchers interested in probability theory and applications to statistical physics.
Table of Contents
- The time constant and the limit shape
- Fluctuations and concentration bounds
- Busemann functions
- Growth and competition models
- Variants of FPP and related models
- Summary of open questions