Asymptotic Geometric Analysis Part Ii

Author : Shiri Artstein-Avidan,Apostolos Giannopoulos,Vitali D. Milman
Publisher : American Mathematical Society
Page : 645 pages
File Size : 55,8 Mb
Release : 2021-12-13
Category : Mathematics
ISBN : 9781470463601

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Asymptotic Geometric Analysis, Part II by Shiri Artstein-Avidan,Apostolos Giannopoulos,Vitali D. Milman Pdf

This book is a continuation of Asymptotic Geometric Analysis, Part I, which was published as volume 202 in this series. Asymptotic geometric analysis studies properties of geometric objects, such as normed spaces, convex bodies, or convex functions, when the dimensions of these objects increase to infinity. The asymptotic approach reveals many very novel phenomena which influence other fields in mathematics, especially where a large data set is of main concern, or a number of parameters which becomes uncontrollably large. One of the important features of this new theory is in developing tools which allow studying high parametric families. Among the topics covered in the book are measure concentration, isoperimetric constants of log-concave measures, thin-shell estimates, stochastic localization, the geometry of Gaussian measures, volume inequalities for convex bodies, local theory of Banach spaces, type and cotype, the Banach-Mazur compactum, symmetrizations, restricted invertibility, and functional versions of geometric notions and inequalities.

Author : Monika Ludwig,Vitali D. Milman,Vladimir Pestov,Nicole Tomczak-Jaegermann
Publisher : Springer
Page : 395 pages
File Size : 40,6 Mb
Release : 2013-03-28
Category : Mathematics
ISBN : 1461464056

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Asymptotic Geometric Analysis by Monika Ludwig,Vitali D. Milman,Vladimir Pestov,Nicole Tomczak-Jaegermann Pdf

Asymptotic Geometric Analysis is concerned with the geometric and linear properties of finite dimensional objects, normed spaces, and convex bodies, especially with the asymptotics of their various quantitative parameters as the dimension tends to infinity. The deep geometric, probabilistic, and combinatorial methods developed here are used outside the field in many areas of mathematics and mathematical sciences. The Fields Institute Thematic Program in the Fall of 2010 continued an established tradition of previous large-scale programs devoted to the same general research direction. The main directions of the program included: * Asymptotic theory of convexity and normed spaces * Concentration of measure and isoperimetric inequalities, optimal transportation approach * Applications of the concept of concentration * Connections with transformation groups and Ramsey theory * Geometrization of probability * Random matrices * Connection with asymptotic combinatorics and complexity theory These directions are represented in this volume and reflect the present state of this important area of research. It will be of benefit to researchers working in a wide range of mathematical sciences—in particular functional analysis, combinatorics, convex geometry, dynamical systems, operator algebras, and computer science.

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 47,6 Mb
Release : 2015
Category : Electronic
ISBN : OCLC:1087819363

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Asymptotic Geometric Analysis by Anonim Pdf

Author : Guillaume Aubrun,Stanisław J. Szarek
Publisher : American Mathematical Soc.
Page : 414 pages
File Size : 42,6 Mb
Release : 2017-08-30
Category : Functional analysis
ISBN : 9781470434687

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Alice and Bob Meet Banach: The Interface of Asymptotic Geometric Analysis and Quantum Information Theory by Guillaume Aubrun,Stanisław J. Szarek Pdf

The quest to build a quantum computer is arguably one of the major scientific and technological challenges of the twenty-first century, and quantum information theory (QIT) provides the mathematical framework for that quest. Over the last dozen or so years, it has become clear that quantum information theory is closely linked to geometric functional analysis (Banach space theory, operator spaces, high-dimensional probability), a field also known as asymptotic geometric analysis (AGA). In a nutshell, asymptotic geometric analysis investigates quantitative properties of convex sets, or other geometric structures, and their approximate symmetries as the dimension becomes large. This makes it especially relevant to quantum theory, where systems consisting of just a few particles naturally lead to models whose dimension is in the thousands, or even in the billions. Alice and Bob Meet Banach is aimed at multiple audiences connected through their interest in the interface of QIT and AGA: at quantum information researchers who want to learn AGA or apply its tools; at mathematicians interested in learning QIT, or at least the part of QIT that is relevant to functional analysis/convex geometry/random matrix theory and related areas; and at beginning researchers in either field. Moreover, this user-friendly book contains numerous tables and explicit estimates, with reasonable constants when possible, which make it a useful reference even for established mathematicians generally familiar with the subject.

Author : Keith M. Ball,Vitali Milman
Publisher : Cambridge University Press
Page : 260 pages
File Size : 54,6 Mb
Release : 1999-01-28
Category : Mathematics
ISBN : 0521642590

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Convex Geometric Analysis by Keith M. Ball,Vitali Milman Pdf

Articles on classical convex geometry, geometric functional analysis, computational geometry, and related areas of harmonic analysis, first published in 1999.

Author : F. Verhulst
Publisher : Unknown
Page : 504 pages
File Size : 53,8 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 366217474X

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Asymptotic Analysis II by F. Verhulst Pdf

Author : Alexander Koldobsky,Alexander Volberg
Publisher : Walter de Gruyter GmbH & Co KG
Page : 608 pages
File Size : 43,5 Mb
Release : 2023-07-24
Category : Mathematics
ISBN : 9783110775433

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Harmonic Analysis and Convexity by Alexander Koldobsky,Alexander Volberg Pdf

In recent years, the interaction between harmonic analysis and convex geometry has increased which has resulted in solutions to several long-standing problems. This collection is based on the topics discussed during the Research Semester on Harmonic Analysis and Convexity at the Institute for Computational and Experimental Research in Mathematics in Providence RI in Fall 2022. The volume brings together experts working in related fields to report on the status of major problems in the area including the isomorphic Busemann-Petty and slicing problems for arbitrary measures, extremal problems for Fourier extension and extremal problems for classical singular integrals of martingale type, among others.

Author : F. Verhulst
Publisher : Springer
Page : 503 pages
File Size : 49,7 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540396123

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Asymptotic Analysis II by F. Verhulst Pdf

Author : Shiri Artstein-Avidan,Gabriele Bianchi,Andrea Colesanti,Paolo Gronchi,Daniel Hug,Monika Ludwig,Fabian Mussnig
Publisher : Springer Nature
Page : 304 pages
File Size : 52,9 Mb
Release : 2023-12-13
Category : Mathematics
ISBN : 9783031378836

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Convex Geometry by Shiri Artstein-Avidan,Gabriele Bianchi,Andrea Colesanti,Paolo Gronchi,Daniel Hug,Monika Ludwig,Fabian Mussnig Pdf

This book collects the lecture notes of the Summer School on Convex Geometry, held in Cetraro, Italy, from August 30th to September 3rd, 2021. Convex geometry is a very active area in mathematics with a solid tradition and a promising future. Its main objects of study are convex bodies, that is, compact and convex subsets of n-dimensional Euclidean space. The so-called Brunn--Minkowski theory currently represents the central part of convex geometry. The Summer School provided an introduction to various aspects of convex geometry: The theory of valuations, including its recent developments concerning valuations on function spaces; geometric and analytic inequalities, including those which come from the Lp Brunn--Minkowski theory; geometric and analytic notions of duality, along with their interplay with mass transportation and concentration phenomena; symmetrizations, which provide one of the main tools to many variational problems (not only in convex geometry). Each of these parts is represented by one of the courses given during the Summer School and corresponds to one of the chapters of the present volume. The initial chapter contains some basic notions in convex geometry, which form a common background for the subsequent chapters. The material of this book is essentially self-contained and, like the Summer School, is addressed to PhD and post-doctoral students and to all researchers approaching convex geometry for the first time.

Author : Ellen Elizabeth Eischen,Wee Teck Gan,Aaron Pollack,Zhiwei Yun
Publisher : American Mathematical Society
Page : 199 pages
File Size : 42,8 Mb
Release : 2024-03-26
Category : Mathematics
ISBN : 9781470474928

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Automorphic Forms Beyond $mathrm {GL}_2$ by Ellen Elizabeth Eischen,Wee Teck Gan,Aaron Pollack,Zhiwei Yun Pdf

The Langlands program has been a very active and central field in mathematics ever since its conception over 50 years ago. It connects number theory, representation theory and arithmetic geometry, and other fields in a profound way. There are nevertheless very few expository accounts beyond the GL(2) case. This book features expository accounts of several topics on automorphic forms on higher rank groups, including rationality questions on unitary group, theta lifts and their applications to Arthur's conjectures, quaternionic modular forms, and automorphic forms over functions fields and their applications to inverse Galois problems. It is based on the lecture notes prepared for the twenty-fifth Arizona Winter School on “Automorphic Forms beyond GL(2)”, held March 5–9, 2022, at the University of Arizona in Tucson. The speakers were Ellen Eischen, Wee Teck Gan, Aaron Pollack, and Zhiwei Yun. The exposition of the book is in a style accessible to students entering the field. Advanced graduate students as well as researchers will find this a valuable introduction to various important and very active research areas.

Author : Ralph S. Freese,Ralph N. McKenzie,George F. McNulty,Walter F. Taylor
Publisher : American Mathematical Society
Page : 451 pages
File Size : 53,7 Mb
Release : 2022-11-03
Category : Mathematics
ISBN : 9781470467982

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Algebras, Lattices, Varieties by Ralph S. Freese,Ralph N. McKenzie,George F. McNulty,Walter F. Taylor Pdf

This book is the third of a three-volume set of books on the theory of algebras, a study that provides a consistent framework for understanding algebraic systems, including groups, rings, modules, semigroups and lattices. Volume I, first published in the 1980s, built the foundations of the theory and is considered to be a classic in this field. The long-awaited volumes II and III are now available. Taken together, the three volumes provide a comprehensive picture of the state of art in general algebra today, and serve as a valuable resource for anyone working in the general theory of algebraic systems or in related fields. The two new volumes are arranged around six themes first introduced in Volume I. Volume II covers the Classification of Varieties, Equational Logic, and Rudiments of Model Theory, and Volume III covers Finite Algebras and their Clones, Abstract Clone Theory, and the Commutator. These topics are presented in six chapters with independent expositions, but are linked by themes and motifs that run through all three volumes.

Author : Gennadiy Feldman
Publisher : American Mathematical Society
Page : 253 pages
File Size : 48,8 Mb
Release : 2023-04-07
Category : Mathematics
ISBN : 9781470472955

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Characterization of Probability Distributions on Locally Compact Abelian Groups by Gennadiy Feldman Pdf

It is well known that if two independent identically distributed random variables are Gaussian, then their sum and difference are also independent. It turns out that only Gaussian random variables have such property. This statement, known as the famous Kac-Bernstein theorem, is a typical example of a so-called characterization theorem. Characterization theorems in mathematical statistics are statements in which the description of possible distributions of random variables follows from properties of some functions of these random variables. The first results in this area are associated with famous 20th century mathematicians such as G. Pólya, M. Kac, S. N. Bernstein, and Yu. V. Linnik. By now, the corresponding theory on the real line has basically been constructed. The problem of extending the classical characterization theorems to various algebraic structures has been actively studied in recent decades. The purpose of this book is to provide a comprehensive and self-contained overview of the current state of the theory of characterization problems on locally compact Abelian groups. The book will be useful to everyone with some familiarity of abstract harmonic analysis who is interested in probability distributions and functional equations on groups.

Author : Anonim
Publisher : Springer Science & Business Media
Page : 444 pages
File Size : 42,8 Mb
Release : 2003
Category : Banach spaces
ISBN : 3540004858

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Geometric Aspects of Functional Analysis by Anonim Pdf

Author : Tadashi Ochiai
Publisher : American Mathematical Society
Page : 167 pages
File Size : 49,5 Mb
Release : 2023-05-03
Category : Mathematics
ISBN : 9781470456726

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Iwasawa Theory and Its Perspective, Volume 1 by Tadashi Ochiai Pdf

Iwasawa theory began in the late 1950s with a series of papers by Kenkichi Iwasawa on ideal class groups in the cyclotomic tower of number fields and their relation to $p$-adic $L$-functions. The theory was later generalized by putting it in the context of elliptic curves and modular forms. The main motivation for writing this book was the need for a total perspective of Iwasawa theory that includes the new trends of generalized Iwasawa theory. Another motivation of this book is an update of the classical theory for class groups taking into account the changed point of view on Iwasawa theory. The goal of this first part of the two-part publication is to explain the theory of ideal class groups, including its algebraic aspect (the Iwasawa class number formula), its analytic aspect (Leopoldt–Kubota $L$-functions), and the Iwasawa main conjecture, which is a bridge between the algebraic and the analytic aspects. The second part of the book will be published as a separate volume in the same series, Mathematical Surveys and Monographs of the American Mathematical Society.

Author : Ronen Eldan,Bo'az Klartag,Alexander Litvak,Emanuel Milman
Publisher : Springer Nature
Page : 443 pages
File Size : 48,5 Mb
Release : 2023-11-01
Category : Mathematics
ISBN : 9783031263002

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Geometric Aspects of Functional Analysis by Ronen Eldan,Bo'az Klartag,Alexander Litvak,Emanuel Milman Pdf

This book reflects general trends in the study of geometric aspects of functional analysis, understood in a broad sense. A classical theme in the local theory of Banach spaces is the study of probability measures in high dimension and the concentration of measure phenomenon. Here this phenomenon is approached from different angles, including through analysis on the Hamming cube, and via quantitative estimates in the Central Limit Theorem under thin-shell and related assumptions. Classical convexity theory plays a central role in this volume, as well as the study of geometric inequalities. These inequalities, which are somewhat in spirit of the Brunn-Minkowski inequality, in turn shed light on convexity and on the geometry of Euclidean space. Probability measures with convexity or curvature properties, such as log-concave distributions, occupy an equally central role and arise in the study of Gaussian measures and non-trivial properties of the heat flow in Euclidean spaces. Also discussed are interactions of this circle of ideas with linear programming and sampling algorithms, including the solution of a question in online learning algorithms using a classical convexity construction from the 19th century.