Random Growth Models
About this Title
Michael Damron, Georgia Institute of Technology, Atlanta, GA, Firas Rassoul-Agha, University of Utah, Salt Lake City, UT and Timo Seppäläinen, University of Wisconsin, Madison, WI, Editors
Publication: Proceedings of Symposia in Applied Mathematics
Publication Year: 2018; Volume 75
ISBNs: 978-1-4704-3553-0 (print); 978-1-4704-4907-0 (online)
The study of random growth models began in probability theory about 50 years ago, and today this area occupies a central place in the subject. The considerable challenges posed by these models have spurred the development of innovative probability theory and opened up connections with several other parts of mathematics, such as partial differential equations, integrable systems, and combinatorics. These models also have applications to fields such as computer science, biology, and physics.
This volume is based on lectures delivered at the 2017 AMS Short Course “Random Growth Models”, held January 2–3, 2017 in Atlanta, GA.
The articles in this book give an introduction to the most-studied models; namely, first- and last-passage percolation, the Eden model of cell growth, and particle systems, focusing on the main research questions and leading up to the celebrated Kardar-Parisi-Zhang equation. Topics covered include asymptotic properties of infection times, limiting shape results, fluctuation bounds, and geometrical properties of geodesics, which are optimal paths for growth.
Graduate Students and researchers interested in various models of random growth in percolation theory, cell growth, and particle systems.
Table of Contents
- Michael Damron – Random growth models: Shape and convergence rate
- Jack Hanson – Infinite geodesics, asymptotic directions, and Busemann functions in first-passage percolation
- Philippe Sosoe – Fluctuations in first-passage percolation
- Firas Rassoul-Agha – Busemann functions, geodesics, and the competition interface for directed last-passage percolation
- Timo Seppäläinen – The corner growth model with exponential weights
- Ivan Corwin – Exactly solving the KPZ equation