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.
Readership
Graduate students and researchers interested in
probability theory and applications to statistical
physics.
