50 years of first-passage percolation

    • Auffinger, Antonio
    • Damron, Michael
    • Hanson, Jack

著者

    • Auffinger, Antonio
    • Damron, Michael
    • Hanson, Jack

書誌事項

50 years of first-passage percolation

Antonio Auffinger, Michael Damron, Jack Hanson

(University lecture series, v. 68)

American Mathematical Society, c2017

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注記

Includes bibliographical references (p. 155-161)

内容説明・目次

内容説明

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.

目次

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.

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