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 Mathematics 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.

Combinatorics And Random Matrix Theory

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Author : Jinho Baik
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-06-22

Combinatorics And Random Matrix Theory written by Jinho Baik 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 2016-06-22 with Mathematics categories.

Over the last fifteen years a variety of problems in combinatorics have been solved in terms of random matrix theory. More precisely, the situation is as follows: the problems at hand are probabilistic in nature and, in an appropriate scaling limit, it turns out that certain key quantities associated with these problems behave statistically like the eigenvalues of a (large) random matrix. Said differently, random matrix theory provides a “stochastic special function theory” for a broad and growing class of problems in combinatorics. The goal of this book is to analyze in detail two key examples of this phenomenon, viz., Ulam's problem for increasing subsequences of random permutations and domino tilings of the Aztec diamond. Other examples are also described along the way, but in less detail. Techniques from many different areas in mathematics are needed to analyze these problems. These areas include combinatorics, probability theory, functional analysis, complex analysis, and the theory of integrable systems. The book is self-contained, and along the way we develop enough of the theory we need from each area that a general reader with, say, two or three years experience in graduate school can learn the subject directly from the text.

Random Polymer Models

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Author : Giambattista Giacomin
language : en
Publisher: Imperial College Press
Release Date : 2007

Random Polymer Models written by Giambattista Giacomin and has been published by Imperial College Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.

Random polymer models and their applications -- The homogeneous pinning model -- Weakly inhomogeneous models -- The free energy of disordered polymer chains -- Disordered pinning models: The hase diagram -- Disordered copolymers and selective interfaces: The phase diagram -- The localized phase of disordered polymers -- The delocalized phase of disordered polymers -- Numerical algorithms and computations

Analysis And Stochastics Of Growth Processes And Interface Models

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Author : Peter Mörters
language : en
Publisher: OUP Oxford
Release Date : 2008-07-24

Analysis And Stochastics Of Growth Processes And Interface Models written by Peter Mörters and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-07-24 with Mathematics categories.

This book is a collection of topical survey articles by leading researchers in the fields of applied analysis and probability theory, working on the mathematical description of growth phenomena. Particular emphasis is on the interplay of the two fields, with articles by analysts being accessible for researchers in probability, and vice versa. Mathematical methods discussed in the book comprise large deviation theory, lace expansion, harmonic multi-scale techniques and homogenisation of partial differential equations. Models based on the physics of individual particles are discussed alongside models based on the continuum description of large collections of particles, and the mathematical theories are used to describe physical phenomena such as droplet formation, Bose-Einstein condensation, Anderson localization, Ostwald ripening, or the formation of the early universe. The combination of articles from the two fields of analysis and probability is highly unusual and makes this book an important resource for researchers working in all areas close to the interface of these fields.

Econometric Analysis Of Cross Section And Panel Data Second Edition

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Author : Jeffrey M. Wooldridge
language : en
Publisher: MIT Press
Release Date : 2010-10-01

Econometric Analysis Of Cross Section And Panel Data Second Edition written by Jeffrey M. Wooldridge and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-10-01 with Business & Economics categories.

The second edition of a comprehensive state-of-the-art graduate level text on microeconometric methods, substantially revised and updated. The second edition of this acclaimed graduate text provides a unified treatment of two methods used in contemporary econometric research, cross section and data panel methods. By focusing on assumptions that can be given behavioral content, the book maintains an appropriate level of rigor while emphasizing intuitive thinking. The analysis covers both linear and nonlinear models, including models with dynamics and/or individual heterogeneity. In addition to general estimation frameworks (particular methods of moments and maximum likelihood), specific linear and nonlinear methods are covered in detail, including probit and logit models and their multivariate, Tobit models, models for count data, censored and missing data schemes, causal (or treatment) effects, and duration analysis. Econometric Analysis of Cross Section and Panel Data was the first graduate econometrics text to focus on microeconomic data structures, allowing assumptions to be separated into population and sampling assumptions. This second edition has been substantially updated and revised. Improvements include a broader class of models for missing data problems; more detailed treatment of cluster problems, an important topic for empirical researchers; expanded discussion of "generalized instrumental variables" (GIV) estimation; new coverage (based on the author's own recent research) of inverse probability weighting; a more complete framework for estimating treatment effects with panel data, and a firmly established link between econometric approaches to nonlinear panel data and the "generalized estimating equation" literature popular in statistics and other fields. New attention is given to explaining when particular econometric methods can be applied; the goal is not only to tell readers what does work, but why certain "obvious" procedures do not. The numerous included exercises, both theoretical and computer-based, allow the reader to extend methods covered in the text and discover new insights.

Individual Tree Diameter Growth Model For Managed Even Aged Upland Oak Stands

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Author : Donald E. Hilt
language : en
Publisher:
Release Date : 1983

Individual Tree Diameter Growth Model For Managed Even Aged Upland Oak Stands written by Donald E. Hilt and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983 with Oak categories.

Growth Modeling

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Author : Kevin J. Grimm
language : en
Publisher: Guilford Publications
Release Date : 2016-10-17

Growth Modeling written by Kevin J. Grimm and has been published by Guilford Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-10-17 with Social Science categories.

Growth models are among the core methods for analyzing how and when people change. Discussing both structural equation and multilevel modeling approaches, this book leads readers step by step through applying each model to longitudinal data to answer particular research questions. It demonstrates cutting-edge ways to describe linear and nonlinear change patterns, examine within-person and between-person differences in change, study change in latent variables, identify leading and lagging indicators of change, evaluate co-occurring patterns of change across multiple variables, and more. User-friendly features include real data examples, code (for Mplus or NLMIXED in SAS, and OpenMx or nlme in R), discussion of the output, and interpretation of each model's results. User-Friendly Features *Real, worked-through longitudinal data examples serving as illustrations in each chapter. *Script boxes that provide code for fitting the models to example data and facilitate application to the reader's own data. *"Important Considerations" sections offering caveats, warnings, and recommendations for the use of specific models. *Companion website supplying datasets and syntax for the book's examples, along with additional code in SAS/R for linear mixed-effects modeling.

City Growth In Europe

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Author : Volker Nitsch
language : en
Publisher: Duncker & Humblot
Release Date : 2015

City Growth In Europe written by Volker Nitsch and has been published by Duncker & Humblot this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with Business & Economics categories.

One of the most notable features of literature about "new economic geography" is a close association between theoretical and empirical work. In contrast to earlier research, theoretical studies are often much more strongly focused on real-world phenomena. At the same time, empirical work is often more closely tied to theoretical models. Instead of purely detecting possible stylized facts, considerable efforts have been made to test for the relevance of theoretical results.A major shortcoming of recent empirical work in urban economics is, however, the startling concentration on basically only two estimation strategies. Probably driven by limited data availability, most analyses are either cross-country studies which usually seek to explore a data set as rich as possible, or the studies examine single country data and then often focus on U.S. experiences.This book aims to provide a new - European - perspective. The basic idea is that a focus on European cities, apart from being interesting for itself, allows to combine both previous approaches. In particular, there is considerable cross-country variation while, in addition, also reliable historical data is available. Therefore, it is one of the contributions to compile a new data set of European cities which covers 13 countries and ranges from 1870 to 1990.This set of data is then applied to explore several hypotheses which have been recently proposed in literature. In particular, three sets of issues are discussed: the growth pattern of cities and their implications for Zipf's law, the relationship between trade openness and urban concentration, and the role of history for city growth. The results are often striking. In contrast to some previous findings, for instance, there is only weak evidence for random growth across cities. Also, the empirical evidence for an association between external trade and internal geography turns out to be shaky. Finally, it is argued that the urban dominance of Vienna after the dissolution of the Austro-Hungarian Empire in 1918 is evidence in favor of path dependence in city growth.Taken together, the book shows that the European experience provides a rich laboratory of real-world data which still waits to be explored. InhaltsverzeichnisInhaltsübersicht: Chapter 1: Introduction - Chapter 2: Some Empirics on Zipf's Law for Cities: Introduction - Theoretical Explanations - Evidence on Zipf's Law in Europe - Distribution Dynamics - The Austrian Experience - Summary - Chapter 3: Krugman and Livas Elizondo Revisited: Is There a Link Between Trade Policy and Urban Concentration?: Introduction - The Model - Simulation Results - Conclusions - Chapter 4: Does Openness Reduce Urban Concentration? Evidence from 120 Years of European Data: Introduction - Potential Causes for Urban Concentration - Data - Results - Conclusion - Chapter 5: Does History Matter for City Growth? The Case of Vienna: Introduction - The Dissolution of the Austro-Hungarian Empire - First Evidence - Probing Deeper - Conclusion - Appendix A-E - Comparing Zipf Exponents for Different Sample Sizes - Examining the Robustness of Eaton and Eckstein's (1997) Results - Replicating Krugman and Livas Elizondo (1996) - Description of the Data - Construction of Openness Measure - References, Data Sources, Subject Index