An Introduction To Random Interlacements

Author : Alexander Drewitz
Publisher : Springer
ISBN 13 : 3319058525
Total Pages : 124 pages
Book Rating : 4.28/5 ( download)

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Download or read book An Introduction to Random Interlacements written by Alexander Drewitz and published by Springer. This book was released on 2014-05-06 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a self-contained introduction to the theory of random interlacements. The intended reader of the book is a graduate student with a background in probability theory who wants to learn about the fundamental results and methods of this rapidly emerging field of research. The model was introduced by Sznitman in 2007 in order to describe the local picture left by the trace of a random walk on a large discrete torus when it runs up to times proportional to the volume of the torus. Random interlacements is a new percolation model on the d-dimensional lattice. The main results covered by the book include the full proof of the local convergence of random walk trace on the torus to random interlacements and the full proof of the percolation phase transition of the vacant set of random interlacements in all dimensions. The reader will become familiar with the techniques relevant to working with the underlying Poisson Process and the method of multi-scale renormalization, which helps in overcoming the challenges posed by the long-range correlations present in the model. The aim is to engage the reader in the world of random interlacements by means of detailed explanations, exercises and heuristics. Each chapter ends with short survey of related results with up-to date pointers to the literature.

Author : Serguei Popov
Publisher : Cambridge University Press
ISBN 13 : 1108472451
Total Pages : 224 pages
Book Rating : 4.56/5 ( download)

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Download or read book Two-Dimensional Random Walk written by Serguei Popov and published by Cambridge University Press. This book was released on 2021-03-18 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: A visual, intuitive introduction in the form of a tour with side-quests, using direct probabilistic insight rather than technical tools.

Author : Maria Eulália Vares
Publisher : Springer Nature
ISBN 13 : 3030607542
Total Pages : 819 pages
Book Rating : 4.48/5 ( download)

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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.

Author : Serguei Popov
Publisher : Cambridge University Press
ISBN 13 : 1108591124
Total Pages : 225 pages
Book Rating : 4.26/5 ( download)

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Download or read book Two-Dimensional Random Walk written by Serguei Popov and published by Cambridge University Press. This book was released on 2021-03-18 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main subject of this introductory book is simple random walk on the integer lattice, with special attention to the two-dimensional case. This fascinating mathematical object is the point of departure for an intuitive and richly illustrated tour of related topics at the active edge of research. It starts with three different proofs of the recurrence of the two-dimensional walk, via direct combinatorial arguments, electrical networks, and Lyapunov functions. After reviewing some relevant potential-theoretic tools, the reader is guided toward the relatively new topic of random interlacements - which can be viewed as a 'canonical soup' of nearest-neighbour loops through infinity - again with emphasis on two dimensions. On the way, readers will visit conditioned simple random walks - which are the 'noodles' in the soup - and also discover how Poisson processes of infinite objects are constructed and review the recently introduced method of soft local times. Each chapter ends with many exercises, making it suitable for courses and independent study.

Author : Serguei Popov
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.48/5 ( download)

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Download or read book Two-dimensional Random Walk written by Serguei Popov and published by . This book was released on 2021 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The main subject of this introductory book is simple random walk on the integer lattice, with special attention to the two-dimensional case. This fascinating mathematical object is the point of departure for an intuitive and richly illustrated tour of related topics at the active edge of research. The book starts with three different proofs of the recurrence of the two-dimensional walk, via direct combinatorial arguments, electrical networks, and Lyapunov functions. Then, after reviewing some relevant potential-theoretic tools, the reader is guided toward the relatively new topic of random interlacements -- which can be viewed as a "canonical soup" of nearest-neighbour loops through infinity -- again with emphasis on two dimensions. On the way, readers will visit conditioned simple random walks -- which are the "noodles" in the soup -- and also discover how Poisson processes of infinite objects are constructed and review the recently introduced method of soft local times. Each chapter ends with many exercises, making the book suitable for courses and for independent study"--

Author : Markus Heydenreich
Publisher : Springer
ISBN 13 : 3319624733
Total Pages : 285 pages
Book Rating : 4.30/5 ( download)

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Download or read book Progress in High-Dimensional Percolation and Random Graphs written by Markus Heydenreich and published by Springer. This book was released on 2017-11-22 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text presents an engaging exposition of the active field of high-dimensional percolation that will likely provide an impetus for future work. With over 90 exercises designed to enhance the reader’s understanding of the material, as well as many open problems, the book is aimed at graduate students and researchers who wish to enter the world of this rich topic. The text may also be useful in advanced courses and seminars, as well as for reference and individual study. Part I, consisting of 3 chapters, presents a general introduction to percolation, stating the main results, defining the central objects, and proving its main properties. No prior knowledge of percolation is assumed. Part II, consisting of Chapters 4–9, discusses mean-field critical behavior by describing the two main techniques used, namely, differential inequalities and the lace expansion. In Parts I and II, all results are proved, making this the first self-contained text discussing high-dime nsional percolation. Part III, consisting of Chapters 10–13, describes recent progress in high-dimensional percolation. Partial proofs and substantial overviews of how the proofs are obtained are given. In many of these results, the lace expansion and differential inequalities or their discrete analogues are central. Part IV, consisting of Chapters 14–16, features related models and further open problems, with a focus on the big picture.

Author : Russell Lyons
Publisher : Cambridge University Press
ISBN 13 : 1316785335
Total Pages : 1023 pages
Book Rating : 4.31/5 ( download)

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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.

Author : Augusto Teixeira
Publisher :
ISBN 13 :
Total Pages : 120 pages
Book Rating : 4.56/5 ( download)

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Download or read book Percolative Properties of Random Interlacements written by Augusto Teixeira and published by . This book was released on 2010 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Tullio Ceccherini-Silberstein
Publisher : Cambridge University Press
ISBN 13 : 1316604403
Total Pages : 539 pages
Book Rating : 4.03/5 ( download)

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Download or read book Groups, Graphs and Random Walks written by Tullio Ceccherini-Silberstein and published by Cambridge University Press. This book was released on 2017-06-29 with total page 539 pages. Available in PDF, EPUB and Kindle. Book excerpt: An up-to-date, panoramic account of the theory of random walks on groups and graphs, outlining connections with various mathematical fields.

Author : Elizabeth S. Meckes
Publisher : Cambridge University Press
ISBN 13 : 1108317995
Total Pages : 225 pages
Book Rating : 4.93/5 ( download)

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Download or read book The Random Matrix Theory of the Classical Compact Groups written by Elizabeth S. Meckes and published by Cambridge University Press. This book was released on 2019-08-01 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book to provide a comprehensive overview of foundational results and recent progress in the study of random matrices from the classical compact groups, drawing on the subject's deep connections to geometry, analysis, algebra, physics, and statistics. The book sets a foundation with an introduction to the groups themselves and six different constructions of Haar measure. Classical and recent results are then presented in a digested, accessible form, including the following: results on the joint distributions of the entries; an extensive treatment of eigenvalue distributions, including the Weyl integration formula, moment formulae, and limit theorems and large deviations for the spectral measures; concentration of measure with applications both within random matrix theory and in high dimensional geometry; and results on characteristic polynomials with connections to the Riemann zeta function. This book will be a useful reference for researchers and an accessible introduction for students in related fields.