Branching Random Walks In Nonhomogenous Environments
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Branching Random Walks
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Author : Zhan Shi
language : en
Publisher: Springer
Release Date : 2016-02-04
Branching Random Walks written by Zhan Shi and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-02-04 with Mathematics categories.
Providing an elementary introduction to branching random walks, the main focus of these lecture notes is on the asymptotic properties of one-dimensional discrete-time supercritical branching random walks, and in particular, on extreme positions in each generation, as well as the evolution of these positions over time. Starting with the simple case of Galton-Watson trees, the text primarily concentrates on exploiting, in various contexts, the spinal structure of branching random walks. The notes end with some applications to biased random walks on trees.
Branching Random Walks In Nonhomogenous Environments
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Author : Elena Yarovaya
language : en
Publisher: John Wiley & Sons
Release Date : 2023-06-14
Branching Random Walks In Nonhomogenous Environments written by Elena Yarovaya and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-06-14 with Science categories.
The book is devoted to a modern section of the probability theory, the so-called theory of branching random walks. Chapter 1 describes the random walk model in the finite branching one-source environment. Chapter 2 is devoted to a model of homogeneous, symmetrical, irreducible random walk (without branching) with finite variance of the jumps on the multidimensional integer continuous-time lattice where transition is possible to an arbitrary point of the lattice and not only to the neighbor state. This model is a generalization of the simple symmetrical random walk often encountered in the applied studies. In Chapter 3 the branching random walk is studied by means of the spectral methods. Here, the property of monotonicity of the mean number of particles in the source plays an important role in the subsequent parts of the book. Chapter 4 demonstrates that existence of an isolated positive eigenvalue in the spectrum of unperturbed random walk generator defines the exponential growth of the process in the supercritical case. Chapter 5 exemplify application of the Tauberian theorems in the asymptotical problems of the probability theory. At last, the final Chapters 6 and 7 are devoted to detailed examination of survival probabilities in the critical and subcritical cases.
Recent Developments In Stochastic Methods And Applications
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Author : Albert N. Shiryaev
language : en
Publisher: Springer Nature
Release Date : 2021-08-02
Recent Developments In Stochastic Methods And Applications written by Albert N. Shiryaev and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-08-02 with Mathematics categories.
Highlighting the latest advances in stochastic analysis and its applications, this volume collects carefully selected and peer-reviewed papers from the 5th International Conference on Stochastic Methods (ICSM-5), held in Moscow, Russia, November 23-27, 2020. The contributions deal with diverse topics such as stochastic analysis, stochastic methods in computer science, analytical modeling, asymptotic methods and limit theorems, Markov processes, martingales, insurance and financial mathematics, queueing theory and stochastic networks, reliability theory, risk analysis, statistical methods and applications, machine learning and data analysis. The 29 articles in this volume are a representative sample of the 87 high-quality papers accepted and presented during the conference. The aim of the ICSM-5 conference is to promote the collaboration of researchers from Russia and all over the world, and to contribute to the development of the field of stochastic analysis and applications of stochastic models.
Random Walks Random Fields And Disordered Systems
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Author : Anton Bovier
language : en
Publisher: Springer
Release Date : 2015-09-21
Random Walks Random Fields And Disordered Systems written by Anton Bovier and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-09-21 with Science categories.
Focusing on the mathematics that lies at the intersection of probability theory, statistical physics, combinatorics and computer science, this volume collects together lecture notes on recent developments in the area. The common ground of these subjects is perhaps best described by the three terms in the title: Random Walks, Random Fields and Disordered Systems. The specific topics covered include a study of Branching Brownian Motion from the perspective of disordered (spin-glass) systems, a detailed analysis of weakly self-avoiding random walks in four spatial dimensions via methods of field theory and the renormalization group, a study of phase transitions in disordered discrete structures using a rigorous version of the cavity method, a survey of recent work on interacting polymers in the ballisticity regime and, finally, a treatise on two-dimensional loop-soup models and their connection to conformally invariant systems and the Gaussian Free Field. The notes are aimed at early graduate students with a modest background in probability and mathematical physics, although they could also be enjoyed by seasoned researchers interested in learning about recent advances in the above fields.
Discrete Time Branching Processes In Random Environment
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Author : Götz Kersting
language : en
Publisher: John Wiley & Sons
Release Date : 2017-11-29
Discrete Time Branching Processes In Random Environment written by Götz Kersting and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-29 with Mathematics categories.
Branching processes are stochastic processes which represent the reproduction of particles, such as individuals within a population, and thereby model demographic stochasticity. In branching processes in random environment (BPREs), additional environmental stochasticity is incorporated, meaning that the conditions of reproduction may vary in a random fashion from one generation to the next. This book offers an introduction to the basics of BPREs and then presents the cases of critical and subcritical processes in detail, the latter dividing into weakly, intermediate, and strongly subcritical regimes.
Branching Processes And Their Applications
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Author : Inés M. del Puerto
language : en
Publisher: Springer
Release Date : 2016-09-06
Branching Processes And Their Applications written by Inés M. del Puerto and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-09-06 with Mathematics categories.
This volume gathers papers originally presented at the 3rd Workshop on Branching Processes and their Applications (WBPA15), which was held from 7 to 10 April 2015 in Badajoz, Spain (http://branching.unex.es/wbpa15/index.htm). The papers address a broad range of theoretical and practical aspects of branching process theory. Further, they amply demonstrate that the theoretical research in this area remains vital and topical, as well as the relevance of branching concepts in the development of theoretical approaches to solving new problems in applied fields such as Epidemiology, Biology, Genetics, and, of course, Population Dynamics. The topics covered can broadly be classified into the following areas: 1. Coalescent Branching Processes 2. Branching Random Walks 3. Population Growth Models in Varying and Random Environments 4. Size/Density/Resource-Dependent Branching Models 5. Age-Dependent Branching Models 6. Special Branching Models 7. Applications in Epidemiology 8. Applications in Biology and Genetics Offering a valuable reference guide to contemporary branching process theory, the book also explores many open problems, paving the way for future research.
Directed Polymers In Random Environments
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Author : Francis Comets
language : en
Publisher: Springer
Release Date : 2017-01-26
Directed Polymers In Random Environments written by Francis Comets and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-01-26 with Mathematics categories.
Analyzing the phase transition from diffusive to localized behavior in a model of directed polymers in a random environment, this volume places particular emphasis on the localization phenomenon. The main questionis: What does the path of a random walk look like if rewards and penalties are spatially randomly distributed?This model, which provides a simplified version of stretched elastic chains pinned by random impurities, has attracted much research activity, but it (and its relatives) still holds many secrets, especially in high dimensions. It has non-gaussian scaling limits and it belongs to the so-called KPZ universality class when the space is one-dimensional. Adopting a Gibbsian approach, using general and powerful tools from probability theory, the discrete model is studied in full generality. Presenting the state-of-the art from different perspectives, and written in the form of a first course on the subject, this monograph is aimed at researchers in probability or statistical physics, but is also accessible to masters and Ph.D. students.
Non Homogeneous Random Walks
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Author : Mikhail Vasilʹevich Menʹshikov
language : en
Publisher:
Release Date : 2017
Non Homogeneous Random Walks written by Mikhail Vasilʹevich Menʹshikov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with MATHEMATICS categories.
Stochastic Interacting Systems Contact Voter And Exclusion Processes
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Author : Thomas M. Liggett
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Stochastic Interacting Systems Contact Voter And Exclusion Processes written by Thomas M. Liggett and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
Interactive Particle Systems is a branch of Probability Theory with close connections to Mathematical Physics and Mathematical Biology. In 1985, the author wrote a book (T. Liggett, Interacting Particle System, ISBN 3-540-96069) that treated the subject as it was at that time. The present book takes three of the most important models in the area, and traces advances in our understanding of them since 1985. In so doing, many of the most useful techniques in the field are explained and developed, so that they can be applied to other models and in other contexts. Extensive Notes and References sections discuss other work on these and related models. Readers are expected to be familiar with analysis and probability at the graduate level, but it is not assumed that they have mastered the material in the 1985 book. This book is intended for graduate students and researchers in Probability Theory, and in related areas of Mathematics, Biology and Physics.
Advances In Disordered Systems Random Processes And Some Applications
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Author : Pierluigi Contucci
language : en
Publisher: Cambridge University Press
Release Date : 2017
Advances In Disordered Systems Random Processes And Some Applications written by Pierluigi Contucci and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with Science categories.
This book offers a unified perspective on the study of complex systems with contributions written by leading scientists from various disciplines, including mathematics, physics, computer science, biology, economics and social science. It is written for researchers from a broad range of scientific fields with an interest in recent developments in complex systems.