Description

Book Synopsis
Describes the main results of first-passage percolation (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 tools from metric geometry, applications of concentration of measure, and related growth and competition models.

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.

    50 Years of FirstPassage Percolation

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      Order before 4pm today for delivery by Thu 25 Jun 2026.

      A Paperback by Antonio Auffinger, Michael Damron, Jack Hanson

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        Publisher: MP-AMM American Mathematical
        Publication Date: 1/30/2018 12:00:00 AM
        ISBN13: 9781470441838, 978-1470441838
        ISBN10: 1470441837

        Description

        Book Synopsis
        Describes the main results of first-passage percolation (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 tools from metric geometry, applications of concentration of measure, and related growth and competition models.

        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.

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