The study of random growth models began in probability theory about 50 years ago, and today this area occupies a central place in the subject. The considerable challenges posed by these models have spurred the development of innovative probability theory and opened up connections with several other parts of mathematics, such as partial differential equations, integrable systems, and combinatorics. These models also have applications to fields such as computer science, biology, and physics. This volume is based on lectures delivered at the 2017 AMS Short Course “Random Growth Models”, held January 2–3, 2017 in Atlanta, GA. The articles in this book give an introduction to the most-studied models; namely, first- and last-passage percolation, the Eden model of cell growth, and particle systems, focusing on the main research questions and leading up to the celebrated Kardar-Parisi-Zhang equation. Topics covered include asymptotic properties of infection times, limiting shape results, fluctuation bounds, and geometrical properties of geodesics, which are optimal paths for growth.

An “irresistibly readable” pair of novellas skewering Americans abroad—by the New York Times–bestselling author and National Book Award finalist(The New York Times Book Review). “In a style that is bold, witty, richly detailed, and suffused with a wry subtlety,” Francine Prose offers penetrating portraits of Americans in Europe who have brought all their baggage—ego, ambition, sexual desire—with them (Elle). Guided Tours of Hell When the insecure (and rightfully so) playwright Landau travels from New York to Prague to read at the first annual Kafka conference, he’s certain this is his chance to prove himself—and his work. But he quickly finds himself upstaged by Jiri Krakauer, a charismatic Holocaust survivor whose claim to fame is a long-ago death-camp love affair with Kafka’s sister. On a group tour to the camp-turned-tourist-attraction, Landau sets out to prove that Krakauer is lying—with unexpected results. Three Pigs in Five Days Ambitious young journalist Nina has been stranded in Paris by her editor and sometimes boyfriend, Leo. When he finally shows up, playfully suggesting a romantic tour of the catacombs, prisons, and shadows of the City of Light, the bloom begins to come off the rose for the infatuated Nina—who must ask herself how much of herself she is willing to sacrifice for love.

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.

Contains "The Remnant," "Armageddon," and "Glorious Appearing"

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