An Introduction To Random Interlacements PDF Download
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| Author | : Alexander Drewitz |
| Publisher | : Springer |
| Total Pages | : 124 |
| Release | : 2014-05-06 |
| Genre | : Mathematics |
| ISBN | : 3319058525 |
Download An Introduction to Random Interlacements Book in PDF, ePub and Kindle
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 |
| Total Pages | : 224 |
| Release | : 2021-03-18 |
| Genre | : Mathematics |
| ISBN | : 1108472451 |
Download Two-Dimensional Random Walk Book in PDF, ePub and Kindle
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 |
| Total Pages | : 819 |
| Release | : 2021-03-25 |
| Genre | : Mathematics |
| ISBN | : 3030607542 |
Download In and Out of Equilibrium 3: Celebrating Vladas Sidoravicius Book in PDF, ePub and Kindle
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 |
| Total Pages | : 225 |
| Release | : 2021-03-18 |
| Genre | : Mathematics |
| ISBN | : 1108591124 |
Download Two-Dimensional Random Walk Book in PDF, ePub and Kindle
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 | : Markus Heydenreich |
| Publisher | : Springer |
| Total Pages | : 285 |
| Release | : 2017-11-22 |
| Genre | : Mathematics |
| ISBN | : 3319624733 |
Download Progress in High-Dimensional Percolation and Random Graphs Book in PDF, ePub and Kindle
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 | : Tullio Ceccherini-Silberstein |
| Publisher | : Cambridge University Press |
| Total Pages | : 539 |
| Release | : 2017-06-29 |
| Genre | : Mathematics |
| ISBN | : 1316604403 |
Download Groups, Graphs and Random Walks Book in PDF, ePub and Kindle
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 |
| Total Pages | : 225 |
| Release | : 2019-08-01 |
| Genre | : Mathematics |
| ISBN | : 1108317995 |
Download The Random Matrix Theory of the Classical Compact Groups Book in PDF, ePub and Kindle
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.
| Author | : Véronique Gayrard |
| Publisher | : Springer |
| Total Pages | : 213 |
| Release | : 2015-06-09 |
| Genre | : Mathematics |
| ISBN | : 3319176749 |
Download Correlated Random Systems: Five Different Methods Book in PDF, ePub and Kindle
This volume presents five different methods recently developed to tackle the large scale behavior of highly correlated random systems, such as spin glasses, random polymers, local times and loop soups and random matrices. These methods, presented in a series of lectures delivered within the Jean-Morlet initiative (Spring 2013), play a fundamental role in the current development of probability theory and statistical mechanics. The lectures were: Random Polymers by E. Bolthausen, Spontaneous Replica Symmetry Breaking and Interpolation Methods by F. Guerra, Derrida's Random Energy Models by N. Kistler, Isomorphism Theorems by J. Rosen and Spectral Properties of Wigner Matrices by B. Schlein. This book is the first in a co-edition between the Jean-Morlet Chair at CIRM and the Springer Lecture Notes in Mathematics which aims to collect together courses and lectures on cutting-edge subjects given during the term of the Jean-Morlet Chair, as well as new material produced in its wake. It is targeted at researchers, in particular PhD students and postdocs, working in probability theory and statistical physics.
| Author | : Michael B. Marcus |
| Publisher | : Cambridge University Press |
| Total Pages | : 4 |
| Release | : 2006-07-24 |
| Genre | : Mathematics |
| ISBN | : 1139458833 |
Download Markov Processes, Gaussian Processes, and Local Times Book in PDF, ePub and Kindle
This book was first published in 2006. Written by two of the foremost researchers in the field, this book studies the local times of Markov processes by employing isomorphism theorems that relate them to certain associated Gaussian processes. It builds to this material through self-contained but harmonized 'mini-courses' on the relevant ingredients, which assume only knowledge of measure-theoretic probability. The streamlined selection of topics creates an easy entrance for students and experts in related fields. The book starts by developing the fundamentals of Markov process theory and then of Gaussian process theory, including sample path properties. It then proceeds to more advanced results, bringing the reader to the heart of contemporary research. It presents the remarkable isomorphism theorems of Dynkin and Eisenbaum and then shows how they can be applied to obtain new properties of Markov processes by using well-established techniques in Gaussian process theory. This original, readable book will appeal to both researchers and advanced graduate students.
| Author | : Geoffrey Grimmett |
| Publisher | : Cambridge University Press |
| Total Pages | : 279 |
| Release | : 2018-01-25 |
| Genre | : Mathematics |
| ISBN | : 1108542999 |
Download Probability on Graphs Book in PDF, ePub and Kindle
This introduction to some of the principal models in the theory of disordered systems leads the reader through the basics, to the very edge of contemporary research, with the minimum of technical fuss. Topics covered include random walk, percolation, self-avoiding walk, interacting particle systems, uniform spanning tree, random graphs, as well as the Ising, Potts, and random-cluster models for ferromagnetism, and the Lorentz model for motion in a random medium. This new edition features accounts of major recent progress, including the exact value of the connective constant of the hexagonal lattice, and the critical point of the random-cluster model on the square lattice. The choice of topics is strongly motivated by modern applications, and focuses on areas that merit further research. Accessible to a wide audience of mathematicians and physicists, this book can be used as a graduate course text. Each chapter ends with a range of exercises.
