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.

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http://www.cos.gatech.edu/hg/item/602241

Michael Damron is an Associate Professor in the SoM at Georgia Tech, who has been highly active in the fields of Continuous and Discrete Probability, has been awarded several teaching awards including the LexisNexis Dean’s award from Georgia Tech in 2016, and is mentoring several post-docs and graduate students here at Tech. This is Michael's second book.