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The Parabolic Anderson Model On A Galton Watson Tree
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Book Synopsis The Parabolic Anderson Model on a Galton-Watson Tree by : Frank den Hollander
Download or read book The Parabolic Anderson Model on a Galton-Watson Tree written by Frank den Hollander and published by . This book was released on 2020 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We study the long-time asymptotics of the total mass of the solution to the parabolic Anderson model ( PAM) on a supercritical Galton-Watson random tree with bounded degrees. We identify the second-order contribution to this asymptotics in terms of a variational formula that gives information about the local structure of the region where the solution is concentrated. The analysis behind this formula suggests that, under mild conditions on the model parameters, concentration takes place on a tree with minimal degree. Our approach can be applied to finite locally tree-like random graphs, in a coupled limit where both time and graph size tend to infinity. As an example, we consider the configuration model or, more precisely, the uniform simple random graph with a prescribed degree sequence.
Book Synopsis The Parabolic Anderson Model on Galton-Watson Trees by :
Download or read book The Parabolic Anderson Model on Galton-Watson Trees written by and published by . This book was released on 2024 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis In and Out of Equilibrium 3: Celebrating Vladas Sidoravicius by : Maria Eulália Vares
Download or read book In and Out of Equilibrium 3: Celebrating Vladas Sidoravicius written by Maria Eulália Vares and published by Springer Nature. This book was released on 2021-03-25 with total page 819 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis The Parabolic Anderson Model by : Wolfgang König
Download or read book The Parabolic Anderson Model written by Wolfgang König and published by Birkhäuser. This book was released on 2016-06-30 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a comprehensive survey on the research on the parabolic Anderson model – the heat equation with random potential or the random walk in random potential – of the years 1990 – 2015. The investigation of this model requires a combination of tools from probability (large deviations, extreme-value theory, e.g.) and analysis (spectral theory for the Laplace operator with potential, variational analysis, e.g.). We explain the background, the applications, the questions and the connections with other models and formulate the most relevant results on the long-time behavior of the solution, like quenched and annealed asymptotics for the total mass, intermittency, confinement and concentration properties and mass flow. Furthermore, we explain the most successful proof methods and give a list of open research problems. Proofs are not detailed, but concisely outlined and commented; the formulations of some theorems are slightly simplified for better comprehension.
Book Synopsis Probability and Statistical Physics in St. Petersburg by : V. Sidoravicius
Download or read book Probability and Statistical Physics in St. Petersburg written by V. Sidoravicius and published by American Mathematical Soc.. This book was released on 2016-04-28 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book brings a reader to the cutting edge of several important directions of the contemporary probability theory, which in many cases are strongly motivated by problems in statistical physics. The authors of these articles are leading experts in the field and the reader will get an exceptional panorama of the field from the point of view of scientists who played, and continue to play, a pivotal role in the development of the new methods and ideas, interlinking it with geometry, complex analysis, conformal field theory, etc., making modern probability one of the most vibrant areas in mathematics.
Book Synopsis Probability Theory on Galton-Watson Trees by : Alex Perlin
Download or read book Probability Theory on Galton-Watson Trees written by Alex Perlin and published by . This book was released on 2001 with total page 91 pages. Available in PDF, EPUB and Kindle. Book excerpt: By a Galton-Watson tree T we mean an infinite rooted tree that starts with one node and where each node has a random number of children independently of the rest of the tree. In the first chapter of this thesis, we prove a conjecture made in [7] for Galton-Watson trees where vertices have bounded number of children not equal to 1. The conjecture states that the electric conductance of such a tree has a continuous distribution. In the second chapter, we study rays in Galton-Watson trees. We establish what concentration of vertices with is given number of children is possible along a ray in a typical tree. We also gauge the size of the collection of all rays with given concentrations of vertices of given degrees.
Book Synopsis The Parabolic Anderson Model and Long-range Percolation by :
Download or read book The Parabolic Anderson Model and Long-range Percolation written by and published by . This book was released on 2014 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Contact Process on Trees by : Robin Pemantle
Download or read book The Contact Process on Trees written by Robin Pemantle and published by . This book was released on 1989 with total page 92 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Structural Properties of Galton-Watson Trees by : Marcel Goh
Download or read book Structural Properties of Galton-Watson Trees written by Marcel Goh and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This thesis presents three results concerning conditional Galton--Watson trees.Each of these results involves, in some way, the structure or shape of the underlying tree.First we tackle the root estimation problem in Galton--Watson trees, whose setup is as follows.A Galton--Watson tree is generated with a known offspring distribution, conditioned on its having $n$ nodes.Next, the parent-child directions of the edges are erased, so that only the simple-graph structure of the treeremains. The root estimation problem asks for a maximum-likelihood estimator for the root of the originaltree. We give such an estimator and determine its probability of being correct.Next we study the sizes of orbits of nodes in a conditional Galton--Watson tree under graph automorphism.In the root estimation problem above, it was convenient to define the multiplicity of a nodeto be the size of the node's orbit under (a certain subgroup of) the free tree's automorphism group.The problem of computing the maximum of the multiplicities of the nodes turns out to be rather difficult,so we introduce a finer partition of the nodes and givean asymptotic calculation of thesize of the largest equivalence class under this stricter definition of multiplicity.Finally, we study several parameters of a conditional Galton--Watson tree that are related to independentsets. We give a formula for the independence number of a conditional Galton--Watson tree in terms ofthe offspring generating function of the distribution. We also analyse the running time of a commonly-usedalgorithm that computes the independent set. This corresponds to a structural parameter of the tree thatwe call the peel number and we also consider a similar parameter which we call the leaf height"--
Author :University of Minnesota. Institute for Mathematics and Its Applications Publisher : ISBN 13 : Total Pages :31 pages Book Rating :4.:/5 (123 download)
Book Synopsis Galton-Watson Trees with the Same Mean Have the Same Polar Sets by : University of Minnesota. Institute for Mathematics and Its Applications
Download or read book Galton-Watson Trees with the Same Mean Have the Same Polar Sets written by University of Minnesota. Institute for Mathematics and Its Applications and published by . This book was released on 1994 with total page 31 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Average Properties of Random Walks on Galton-Watson Trees by : Dayue Chen
Download or read book Average Properties of Random Walks on Galton-Watson Trees written by Dayue Chen and published by . This book was released on 1996 with total page 15 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Random Graph Dynamics by : Rick Durrett
Download or read book Random Graph Dynamics written by Rick Durrett and published by Cambridge University Press. This book was released on 2010-05-31 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of random graphs began in the late 1950s in several papers by Erdos and Renyi. In the late twentieth century, the notion of six degrees of separation, meaning that any two people on the planet can be connected by a short chain of people who know each other, inspired Strogatz and Watts to define the small world random graph in which each site is connected to k close neighbors, but also has long-range connections. At a similar time, it was observed in human social and sexual networks and on the Internet that the number of neighbors of an individual or computer has a power law distribution. This inspired Barabasi and Albert to define the preferential attachment model, which has these properties. These two papers have led to an explosion of research. The purpose of this book is to use a wide variety of mathematical argument to obtain insights into the properties of these graphs. A unique feature is the interest in the dynamics of process taking place on the graph in addition to their geometric properties, such as connectedness and diameter.
Book Synopsis Probability on Trees and Networks by : Russell Lyons
Download or read book Probability on Trees and Networks written by Russell Lyons and published by Cambridge University Press. This book was released on 2017-01-20 with total page 1023 pages. Available in PDF, EPUB and Kindle. Book excerpt: Starting around the late 1950s, several research communities began relating the geometry of graphs to stochastic processes on these graphs. This book, twenty years in the making, ties together research in the field, encompassing work on percolation, isoperimetric inequalities, eigenvalues, transition probabilities, and random walks. Written by two leading researchers, the text emphasizes intuition, while giving complete proofs and more than 850 exercises. Many recent developments, in which the authors have played a leading role, are discussed, including percolation on trees and Cayley graphs, uniform spanning forests, the mass-transport technique, and connections on random walks on graphs to embedding in Hilbert space. This state-of-the-art account of probability on networks will be indispensable for graduate students and researchers alike.
Book Synopsis Nonlinear Dynamics in Geosciences by : Anastasios A. Tsonis
Download or read book Nonlinear Dynamics in Geosciences written by Anastasios A. Tsonis and published by Springer Science & Business Media. This book was released on 2007-10-23 with total page 603 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work comprises the proceedings of a conference held last year in Rhodes, Greece, to assess developments during the last 20 years in the field of nonlinear dynamics in geosciences. The volume has its own authority as part of the Aegean Conferences cycle, but it also brings together the most up-to-date research from the atmospheric sciences, hydrology, geology, and other areas of geosciences, and discusses the advances made and the future directions of nonlinear dynamics.
Download or read book Mathematical Reviews written by and published by . This book was released on 2001 with total page 852 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Current Index to Statistics, Applications, Methods and Theory by :
Download or read book Current Index to Statistics, Applications, Methods and Theory written by and published by . This book was released on 1997 with total page 812 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Current Index to Statistics (CIS) is a bibliographic index of publications in statistics, probability, and related fields.
Book Synopsis Quantitative Methods for Investigating Infectious Disease Outbreaks by : Ping Yan
Download or read book Quantitative Methods for Investigating Infectious Disease Outbreaks written by Ping Yan and published by Springer. This book was released on 2019-08-16 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a systematic treatment of the mathematical underpinnings of work in the theory of outbreak dynamics and their control, covering balanced perspectives between theory and practice including new material on contemporary topics in the field of infectious disease modelling. Specifically, it presents a unified mathematical framework linked to the distribution theory of non-negative random variables; the many examples used in the text, are introduced and discussed in light of theoretical perspectives. The book is organized into 9 chapters: The first motivates the presentation of the material on subsequent chapters; Chapter 2-3 provides a review of basic concepts of probability and statistical models for the distributions of continuous lifetime data and the distributions of random counts and counting processes, which are linked to phenomenological models. Chapters 4 focuses on dynamic behaviors of a disease outbreak during the initial phase while Chapters 5-6 broadly cover compartment models to investigate the consequences of epidemics as the outbreak moves beyond the initial phase. Chapter 7 provides a transition between mostly theoretical topics in earlier chapters and Chapters 8 and 9 where the focus is on the data generating processes and statistical issues of fitting models to data as well as specific mathematical epidemic modeling applications, respectively. This book is aimed at a wide audience ranging from graduate students to established scientists from quantitatively-oriented fields of epidemiology, mathematics and statistics. The numerous examples and illustrations make understanding of the mathematics of disease transmission and control accessible. Furthermore, the examples and exercises, make the book suitable for motivated students in applied mathematics, either through a lecture course, or through self-study. This text could be used in graduate schools or special summer schools covering research problems in mathematical biology.
