Random Growth Models

Front Cover
Michael Damron, Firas Rassoul-Agha, Timo Seppäläinen
American Mathematical Soc., Sep 27, 2018 - Mathematics - 256 pages

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.

 

Selected pages

Contents

Shape and convergence rate
1
Infinite geodesics asymptotic directions and Busemann functions in firstpassage percolation
39
Fluctuations in firstpassage percolation
69
Busemann functions geodesics and the competition interface for directed lastpassage percolation
95
The corner growth model with exponential weights
133
Exactly solving the KPZ equation
203
Index
255
Back Cover
263
Copyright

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Random Growth Models
Michael Damron,Firas Rassoul-Agha,Timo Seppäläinen
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Common terms and phrases

argument Assume assumption boundary Brownian motion Busemann functions coalescence cocycle contours convergence convex corner growth model define definition denote e₁ edge weights endpoints ergodic theorem exactly solvable exactly solvable models exists exponentially distributed exponents finite first-passage percolation fixed fluctuations Gx,y implies independent inequality infection infinite geodesics initial data integral Jack Hanson KPZ equation last-passage percolation lattice law of large Lemma limit shape LPP process Lq-Boson Markov process Math maximizing path Michael Damron ne₁ particle passage percolation probability measure probability space proof of Theorem properties prove q-TASEP random variables result satisfies scaling Section sequence shape function shape theorem step stochastic subadditive subadditive ergodic theorem subsequential limit surely TASEP Theorem 3.1 Timo Seppäläinen Tracy-Widom distribution unigeodesics unique upper bound vertices Xo,n

About the author (2018)

Edited by Michael Damron: Georgia Institute of Technology, Atlanta, GA,
Firas Rassoul-Agha: University of Utah, Salt Lake City, UT,
Timo Seppäläinen: University of Wisconsin, Madison, WI

Bibliographic information

TitleRandom Growth Models
Volume 75 of Proceedings of Symposia in Applied Mathematics
EditorsMichael Damron, Firas Rassoul-Agha, Timo Seppäläinen
Editionillustrated
PublisherAmerican Mathematical Soc., 2018
ISBN1470435535, 9781470435530
Length256 pages
Subjects ›  › 

Mathematics / Probability & Statistics / General
Mathematics / Probability & Statistics / Stochastic Processes
Science / Physics / Mathematical & Computational
  
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