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50 Years of First-Passage Percolation

Antonio Auffinger Northwestern University, Evanston, IL
Michael Damron Georgia Institute of Technology, Atlanta, GA
Jack Hanson The City College of New York, New York, NY
Available Formats:
Softcover ISBN: 978-1-4704-4183-8
Product Code: ULECT/68
List Price: $44.00 MAA Member Price:$39.60
AMS Member Price: $35.20 Electronic ISBN: 978-1-4704-4356-6 Product Code: ULECT/68.E List Price:$44.00
MAA Member Price: $39.60 AMS Member Price:$35.20
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List Price: $66.00 MAA Member Price:$59.40
AMS Member Price: $52.80 Click above image for expanded view 50 Years of First-Passage Percolation Antonio Auffinger Northwestern University, Evanston, IL Michael Damron Georgia Institute of Technology, Atlanta, GA Jack Hanson The City College of New York, New York, NY Available Formats:  Softcover ISBN: 978-1-4704-4183-8 Product Code: ULECT/68  List Price:$44.00 MAA Member Price: $39.60 AMS Member Price:$35.20
 Electronic ISBN: 978-1-4704-4356-6 Product Code: ULECT/68.E
 List Price: $44.00 MAA Member Price:$39.60 AMS Member Price: $35.20 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$66.00 MAA Member Price: $59.40 AMS Member Price:$52.80
• Book Details

University Lecture Series
Volume: 682017; 161 pp
MSC: Primary 60; 82;

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.

• Chapters
• Introduction
• The time constant and the limit shape
• Fluctuations and concentration bounds
• Geodesics
• Busemann functions
• Growth and competition models
• Variants of FPP and related models
• Summary of open questions

• Reviews

• [This book] succeeds admirably in providing an authoritative overview of this topic, with complete proofs of the main results and the 190 cited papers, provide some sense of the size of this topic. It will deservedly become the definitive introduction and reference for many years. It could be used as the basis for an advanced graduate course, though there are no exercises.

David Aldous, MAA Reviews
• Requests

Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Volume: 682017; 161 pp
MSC: Primary 60; 82;

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.

• Chapters
• Introduction
• The time constant and the limit shape
• Fluctuations and concentration bounds
• Geodesics
• Busemann functions
• Growth and competition models
• Variants of FPP and related models
• Summary of open questions
• [This book] succeeds admirably in providing an authoritative overview of this topic, with complete proofs of the main results and the 190 cited papers, provide some sense of the size of this topic. It will deservedly become the definitive introduction and reference for many years. It could be used as the basis for an advanced graduate course, though there are no exercises.

David Aldous, MAA Reviews
Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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