50 years of first-passage percolation
Author(s)
Bibliographic Information
50 years of first-passage percolation
（University lecture series, v. 68）
American Mathematical Society, c2017
Available at / 21 libraries
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
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Note
Includes bibliographical references (p. 155-161)
Description and Table of Contents
Description
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.
Table of Contents
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
Bibliography.
by "Nielsen BookData"