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| Hardcover ISBN: | 978-1-4704-3553-0 |
| Product Code: | PSAPM/75 |
| List Price: | $129.00 |
| MAA Member Price: | $116.10 |
| AMS Member Price: | $103.20 |
| eBook ISBN: | 978-1-4704-4907-0 |
| Product Code: | PSAPM/75.E |
| List Price: | $125.00 |
| MAA Member Price: | $112.50 |
| AMS Member Price: | $100.00 |
| Hardcover ISBN: | 978-1-4704-3553-0 |
| eBook ISBN: | 978-1-4704-4907-0 |
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Book DetailsProceedings of Symposia in Applied MathematicsVolume: 75; 2018; 256 ppMSC: Primary 60; 82
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.
ReadershipGraduate Students and researchers interested in various models of random growth in percolation theory, cell growth, and particle systems.
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Table of Contents
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Articles
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Michael Damron — Random growth models: Shape and convergence rate
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Jack Hanson — Infinite geodesics, asymptotic directions, and Busemann functions in first-passage percolation
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Philippe Sosoe — Fluctuations in first-passage percolation
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Firas Rassoul-Agha — Busemann functions, geodesics, and the competition interface for directed last-passage percolation
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Timo Seppäläinen — The corner growth model with exponential weights
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Ivan Corwin — Exactly solving the KPZ equation
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Additional Material
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RequestsReview Copy – for publishers of book reviewsPermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
- Book Details
- Table of Contents
- Additional Material
- Requests
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.
-
Articles
-
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
