Coarse Geometry And Randomness

Author : Itai Benjamini
Publisher : Springer
Page : 133 pages
File Size : 40,8 Mb
Release : 2013-12-02
Category : Mathematics
ISBN : 9783319025766

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Coarse Geometry and Randomness by Itai Benjamini Pdf

These lecture notes study the interplay between randomness and geometry of graphs. The first part of the notes reviews several basic geometric concepts, before moving on to examine the manifestation of the underlying geometry in the behavior of random processes, mostly percolation and random walk. The study of the geometry of infinite vertex transitive graphs, and of Cayley graphs in particular, is fairly well developed. One goal of these notes is to point to some random metric spaces modeled by graphs that turn out to be somewhat exotic, that is, they admit a combination of properties not encountered in the vertex transitive world. These include percolation clusters on vertex transitive graphs, critical clusters, local and scaling limits of graphs, long range percolation, CCCP graphs obtained by contracting percolation clusters on graphs, and stationary random graphs, including the uniform infinite planar triangulation (UIPT) and the stochastic hyperbolic planar quadrangulation (SHIQ).

Author : Itai Benjamini
Publisher : Unknown
Page : 142 pages
File Size : 46,7 Mb
Release : 2013-12-31
Category : Electronic
ISBN : 3319025775

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Coarse Geometry and Randomness by Itai Benjamini Pdf

Author : Anonim
Publisher : Springer Science & Business Media
Page : 263 pages
File Size : 50,9 Mb
Release : 2021
Category : Electronic
ISBN : 9783540693918

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Information Geometry by Anonim Pdf

Author : Michael Krivelevich,Konstantinos Panagiotou,Mathew Penrose
Publisher : Cambridge University Press
Page : 129 pages
File Size : 50,7 Mb
Release : 2016-04-25
Category : Mathematics
ISBN : 9781107136571

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Random Graphs, Geometry and Asymptotic Structure by Michael Krivelevich,Konstantinos Panagiotou,Mathew Penrose Pdf

A concise introduction, aimed at young researchers, to recent developments of a geometric and topological nature in random graphs.

Author : Robert J. Adler
Publisher : SIAM
Page : 295 pages
File Size : 40,7 Mb
Release : 2010-01-28
Category : Mathematics
ISBN : 9780898716931

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The Geometry of Random Fields by Robert J. Adler Pdf

An important treatment of the geometric properties of sets generated by random fields, including a comprehensive treatment of the mathematical basics of random fields in general. It is a standard reference for all researchers with an interest in random fields, whether they be theoreticians or come from applied areas.

Author : Valérie Berthé,Michel Rigo
Publisher : Birkhäuser
Page : 578 pages
File Size : 54,9 Mb
Release : 2018-04-09
Category : Mathematics
ISBN : 9783319691527

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Sequences, Groups, and Number Theory by Valérie Berthé,Michel Rigo Pdf

This collaborative book presents recent trends on the study of sequences, including combinatorics on words and symbolic dynamics, and new interdisciplinary links to group theory and number theory. Other chapters branch out from those areas into subfields of theoretical computer science, such as complexity theory and theory of automata. The book is built around four general themes: number theory and sequences, word combinatorics, normal numbers, and group theory. Those topics are rounded out by investigations into automatic and regular sequences, tilings and theory of computation, discrete dynamical systems, ergodic theory, numeration systems, automaton semigroups, and amenable groups. This volume is intended for use by graduate students or research mathematicians, as well as computer scientists who are working in automata theory and formal language theory. With its organization around unified themes, it would also be appropriate as a supplemental text for graduate level courses.

Author : Andrew Beveridge,Jerrold R. Griggs,Leslie Hogben,Gregg Musiker,Prasad Tetali
Publisher : Springer
Page : 778 pages
File Size : 40,7 Mb
Release : 2016-04-12
Category : Mathematics
ISBN : 9783319242989

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Recent Trends in Combinatorics by Andrew Beveridge,Jerrold R. Griggs,Leslie Hogben,Gregg Musiker,Prasad Tetali Pdf

This volume presents some of the research topics discussed at the 2014-2015 Annual Thematic Program Discrete Structures: Analysis and Applications at the Institute for Mathematics and its Applications during Fall 2014, when combinatorics was the focus. Leading experts have written surveys of research problems, making state of the art results more conveniently and widely available. The three-part structure of the volume reflects the three workshops held during Fall 2014. In the first part, topics on extremal and probabilistic combinatorics are presented; part two focuses on additive and analytic combinatorics; and part three presents topics in geometric and enumerative combinatorics. This book will be of use to those who research combinatorics directly or apply combinatorial methods to other fields.

Author : Georges Matheron
Publisher : John Wiley & Sons
Page : 294 pages
File Size : 48,8 Mb
Release : 1974
Category : Mathematics
ISBN : UOM:39015038937648

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Random Sets and Integral Geometry by Georges Matheron Pdf

Author : Christian Rosendal
Publisher : Cambridge University Press
Page : 309 pages
File Size : 46,9 Mb
Release : 2021-12-16
Category : Mathematics
ISBN : 9781108842471

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Coarse Geometry of Topological Groups by Christian Rosendal Pdf

Provides a general framework for doing geometric group theory for non-locally-compact topological groups arising in mathematical practice.

Author : Patrick Bourdot,Sue Cobb,Victoria Interrante,Hirokazu kato,Didier Stricker
Publisher : Springer
Page : 261 pages
File Size : 40,8 Mb
Release : 2018-10-15
Category : Computers
ISBN : 9783030017903

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Virtual Reality and Augmented Reality by Patrick Bourdot,Sue Cobb,Victoria Interrante,Hirokazu kato,Didier Stricker Pdf

This book constitutes the refereed proceedings of the 15th International Conference on Virtual Reality and Augmented Reality, EuroVR 2018, held in London, UK, in October 2018. The 9 full papers and 6 short papers presented were carefully reviewed and selected from 39 submissions. The papers are organized in 5topical sections: vision-based motion tracking; 3D acquisition and 3D reconstruction; haptics and 3D audio; perception and cognition; interactive techniques and use-case studies.

Author : Robert Adler,Jonathan E. Taylor
Publisher : Springer Science & Business Media
Page : 135 pages
File Size : 42,9 Mb
Release : 2011-05-18
Category : Mathematics
ISBN : 9783642195792

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Topological Complexity of Smooth Random Functions by Robert Adler,Jonathan E. Taylor Pdf

These notes, based on lectures delivered in Saint Flour, provide an easy introduction to the authors’ 2007 Springer monograph “Random Fields and Geometry.” While not as exhaustive as the full monograph, they are also less exhausting, while still covering the basic material, typically at a more intuitive and less technical level. They also cover some more recent material relating to random algebraic topology and statistical applications. The notes include an introduction to the general theory of Gaussian random fields, treating classical topics such as continuity and boundedness. This is followed by a quick review of geometry, both integral and Riemannian, with an emphasis on tube formulae, to provide the reader with the material needed to understand and use the Gaussian kinematic formula, the main result of the notes. This is followed by chapters on topological inference and random algebraic topology, both of which provide applications of the main results.

Author : Frédérique Bassino,Ilya Kapovich,Markus Lohrey,Alexei Miasnikov,Cyril Nicaud,Andrey Nikolaev,Igor Rivin,Vladimir Shpilrain,Alexander Ushakov,Pascal Weil
Publisher : Walter de Gruyter GmbH & Co KG
Page : 412 pages
File Size : 54,8 Mb
Release : 2020-06-08
Category : Mathematics
ISBN : 9783110667523

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Complexity and Randomness in Group Theory by Frédérique Bassino,Ilya Kapovich,Markus Lohrey,Alexei Miasnikov,Cyril Nicaud,Andrey Nikolaev,Igor Rivin,Vladimir Shpilrain,Alexander Ushakov,Pascal Weil Pdf

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Author : John Roe
Publisher : American Mathematical Soc.
Page : 184 pages
File Size : 41,6 Mb
Release : 2003
Category : Mathematics
ISBN : 9780821833322

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Lectures on Coarse Geometry by John Roe Pdf

Coarse geometry is the study of spaces (particularly metric spaces) from a 'large scale' point of view, so that two spaces that look the same from a great distance are actually equivalent. This book provides a general perspective on coarse structures. It discusses results on asymptotic dimension and uniform embeddings into Hilbert space.

Author : Craig D. Hodgson,William H. Jaco,Martin G. Scharlemann,Stephan Tillmann
Publisher : American Mathematical Soc.
Page : 395 pages
File Size : 49,7 Mb
Release : 2013-08-23
Category : Mathematics
ISBN : 9780821884805

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Geometry and Topology Down Under by Craig D. Hodgson,William H. Jaco,Martin G. Scharlemann,Stephan Tillmann Pdf

This book contains the proceedings of the conference Geometry & Topology Down Under, held July 11-22, 2011, at the University of Melbourne, Parkville, Australia, in honour of Hyam Rubinstein. The main topic of the book is low-dimensional geometry and topology. It includes both survey articles based on courses presented at the conferences and research articles devoted to important questions in low-dimensional geometry. Together, these contributions show how methods from different fields of mathematics contribute to the study of 3-manifolds and Gromov hyperbolic groups. It also contains a list of favorite problems by Hyam Rubinstein.

Author : Terence Tao
Publisher : American Mathematical Soc.
Page : 316 pages
File Size : 44,9 Mb
Release : 2024-07-03
Category : Mathematics
ISBN : 0821886282

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Structure and Randomness by Terence Tao Pdf

"In 2007, Terry Tao began a mathematical blog, as an outgrowth of his own website at UCLA. This book is based on a selection of articles from the first year of that blog. These articles discuss a wide range of mathematics and its applications, ranging from expository articles on quantum mechanics, Einstein's equation E = mc[superscript 2], or compressed sensing, to open problems in analysis, combinatorics, geometry, number theory, and algebra, to lecture series on random matrices, Fourier analysis, or the dichotomy between structure and randomness that is present in many subfields of mathematics, to more philosophical discussions on such topics as the interplay between finitary and infinitary in analysis. Some selected commentary from readers of the blog has also been included at the end of each article.