Random Growth Models

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Random Growth Models

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Author : Michael Damron
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-09-27

Random Growth Models written by Michael Damron and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-27 with Random measures categories.

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.

Random Growth Models

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Author : Michael Damron
language : en
Publisher:
Release Date : 2018

Random Growth Models written by Michael Damron and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with Random measures categories.

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 Ja.

Topics In Random Growth Models

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Author : Finn, Thomas
language : en
Publisher:
Release Date : 2021

Topics In Random Growth Models written by Finn, Thomas and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with categories.

Competition Within Random Growth Models

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Author : Shane Turnbull
language : en
Publisher:
Release Date : 2018

Competition Within Random Growth Models written by Shane Turnbull and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with categories.

Degenerate Regimes For Random Growth Models In The Complex Plane

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Author : Frankie Higgs
language : en
Publisher:
Release Date : 2022

Degenerate Regimes For Random Growth Models In The Complex Plane written by Frankie Higgs and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022 with categories.

Random Graph And Growth Models

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Author :
language : en
Publisher:
Release Date : 2020

Random Graph And Growth Models written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020 with categories.

Universality For Some Random Growth Models

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Author : Kevin Yang
language : en
Publisher:
Release Date : 2022

Universality For Some Random Growth Models written by Kevin Yang and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022 with categories.

This thesis studies the problem of deriving fluctuations of hydrodynamic limits for general time-dependent microscopic systems. To this end, we develop a derivation of the Boltzmann-Gibbs principle depending only on the dynamics of the system at hand. This provides an answer to conjectures of Spohn and Jensen-Yau. As an application of the method, we derive the Kardar-Parisi-Zhang equation as a continuum limit of the current fluctuations in some non-integrable and non-stationary asymmetric exclusion processes.

Random Vs Deterministic Initial Conditions In Kpz Growth Models

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Author : Giovanni D'Urso
language : en
Publisher:
Release Date : 2015

Random Vs Deterministic Initial Conditions In Kpz Growth Models written by Giovanni D'Urso and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with categories.

Geodesics In Random Growth Models

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Author : Xiao Shen
language : en
Publisher:
Release Date : 2021

Geodesics In Random Growth Models written by Xiao Shen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with categories.

We study two percolation-type models related to the Kardar-Parisi-Zhang (KPZ) universality class: first-passage percolation (FPP) and exponential corner growth model (CGM). FPP is one of the famous conjectural members of the KPZ class, on the other hand, the CGM is one of its important integrable members. In both models, growth proceeds along optimal paths called geodesics, determined by a random environment. In a joint work with Timo Seppalainen, we establish estimates for the coalescence time of semi-infinite directed geodesics in CGM. There are four estimates: upper and lower bounds on the probabilities of both fast and slow coalescence on the correct spatial scale with exponent 3/2. Our proofs utilize a geodesic duality introduced by Pimentel and properties of the increment-stationary last-passage percolation process. For fast coalescence our bounds are new and they have a matching optimal exponential order of magnitude. For slow coalescence we reproduce bounds proved earlier with integrable probability inputs, except that our upper bound misses the optimal order by a logarithmic factor. In a joint work with Michael Damron, Chris Janjigian and Wai-Kit Lam, we establish tail estimates for the averaged empirical distribution of edge weights along geodesics in first-passage percolation in general dimensions. As an application, we show that if the edge weight distribution has finite positive moments of any order, then any limit point of the averaged empirical distribution of finite geodesics has finite positive moments of all orders.

Deterministic Growth Dispersal Models And Branching Random Walk

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Author : F. M. Dekking
language : en
Publisher:
Release Date : 1993

Deterministic Growth Dispersal Models And Branching Random Walk written by F. M. Dekking and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with categories.