50 Years of First-Passage Percolation

50 Years of First-Passage Percolation PDF

Author: Antonio Auffinger

Publisher: American Mathematical Soc.

Published: 2017-12-20

Total Pages: 161

ISBN-13: 1470441837

DOWNLOAD EBOOK →

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.

Probability on Discrete Structures

Probability on Discrete Structures PDF

Author: Harry Kesten

Publisher: Springer Science & Business Media

Published: 2013-03-14

Total Pages: 358

ISBN-13: 3662094444

DOWNLOAD EBOOK →

Most probability problems involve random variables indexed by space and/or time. These problems almost always have a version in which space and/or time are taken to be discrete. This volume deals with areas in which the discrete version is more natural than the continuous one, perhaps even the only one than can be formulated without complicated constructions and machinery. The 5 papers of this volume discuss problems in which there has been significant progress in the last few years; they are motivated by, or have been developed in parallel with, statistical physics. They include questions about asymptotic shape for stochastic growth models and for random clusters; existence, location and properties of phase transitions; speed of convergence to equilibrium in Markov chains, and in particular for Markov chains based on models with a phase transition; cut-off phenomena for random walks. The articles can be read independently of each other. Their unifying theme is that of models built on discrete spaces or graphs. Such models are often easy to formulate. Correspondingly, the book requires comparatively little previous knowledge of the machinery of probability.

In and Out of Equilibrium 3: Celebrating Vladas Sidoravicius

In and Out of Equilibrium 3: Celebrating Vladas Sidoravicius PDF

Author: Maria Eulália Vares

Publisher: Springer Nature

Published: 2021-03-25

Total Pages: 819

ISBN-13: 3030607542

DOWNLOAD EBOOK →

This is a volume in memory of Vladas Sidoravicius who passed away in 2019. Vladas has edited two volumes appeared in this series ("In and Out of Equilibrium") and is now honored by friends and colleagues with research papers reflecting Vladas' interests and contributions to probability theory.

Lanterna Rally - Theme by Grace Themes