The Resource Random Walks on Reductive Groups, by Yves Benoist, JeanFrançois Quint, (electronic resource)
Random Walks on Reductive Groups, by Yves Benoist, JeanFrançois Quint, (electronic resource)
Resource Information
The item Random Walks on Reductive Groups, by Yves Benoist, JeanFrançois Quint, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in European University Institute.This item is available to borrow from 1 library branch.
Resource Information
The item Random Walks on Reductive Groups, by Yves Benoist, JeanFrançois Quint, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in European University Institute.
This item is available to borrow from 1 library branch.
 Summary
 The classical theory of Random Walks describes the asymptotic behavior of sums of independent identically distributed random real variables. This book explains the generalization of this theory to products of independent identically distributed random matrices with real coefficients. Under the assumption that the action of the matrices is semisimple – or, equivalently, that the Zariski closure of the group generated by these matrices is reductive  and under suitable moment assumptions, it is shown that the norm of the products of such random matrices satisfies a number of classical probabilistic laws. This book includes necessary background on the theory of reductive algebraic groups, probability theory and operator theory, thereby providing a modern introduction to the topic.
 Language
 eng
 Extent
 1 online resource (XI, 323 pages)
 Contents

 Introduction
 Part I The Law of Large Numbers
 Stationary measures
 The Law of Large Numbers
 Linear random walks
 Finite index subsemigroups
 Part II Reductive groups
 Loxodromic elements
 The Jordan projection of semigroups
 Reductive groups and their representations
 Zariski dense subsemigroups
 Random walks on reductive groups
 Part III The Central Limit Theorem
 Transfer operators over contracting actions
 Limit laws for cocycles
 Limit laws for products of random matrices
 Regularity of the stationary measure
 Part IV The Local Limit Theorem
 The Spectrum of the complex transfer operator
 The Local limit theorem for cocycles
 The local limit theorem for products of random matrices
 Part V Appendix
 Convergence of sequences of random variables
 The essential spectrum of bounded operators
 Bibliographical comments
 Isbn
 9783319477213
 Label
 Random Walks on Reductive Groups
 Title
 Random Walks on Reductive Groups
 Statement of responsibility
 by Yves Benoist, JeanFrançois Quint
 Language
 eng
 Summary
 The classical theory of Random Walks describes the asymptotic behavior of sums of independent identically distributed random real variables. This book explains the generalization of this theory to products of independent identically distributed random matrices with real coefficients. Under the assumption that the action of the matrices is semisimple – or, equivalently, that the Zariski closure of the group generated by these matrices is reductive  and under suitable moment assumptions, it is shown that the norm of the products of such random matrices satisfies a number of classical probabilistic laws. This book includes necessary background on the theory of reductive algebraic groups, probability theory and operator theory, thereby providing a modern introduction to the topic.
 Assigning source
 Provided by publisher
 http://library.link/vocab/creatorName
 Benoist, Yves
 Image bit depth
 0
 Literary form
 non fiction
 Nature of contents
 dictionaries
 http://library.link/vocab/relatedWorkOrContributorName
 Quint, JeanFrançois.
 Series statement

 Springer eBooks
 Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics,
 Series volume
 62
 http://library.link/vocab/subjectName

 Mathematics
 Topological groups
 Lie groups
 Dynamics
 Ergodic theory
 Probabilities
 Label
 Random Walks on Reductive Groups, by Yves Benoist, JeanFrançois Quint, (electronic resource)
 Antecedent source
 mixed
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Color
 not applicable
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents
 Introduction  Part I The Law of Large Numbers  Stationary measures  The Law of Large Numbers  Linear random walks  Finite index subsemigroups  Part II Reductive groups  Loxodromic elements  The Jordan projection of semigroups  Reductive groups and their representations  Zariski dense subsemigroups  Random walks on reductive groups  Part III The Central Limit Theorem  Transfer operators over contracting actions  Limit laws for cocycles  Limit laws for products of random matrices  Regularity of the stationary measure  Part IV The Local Limit Theorem  The Spectrum of the complex transfer operator  The Local limit theorem for cocycles  The local limit theorem for products of random matrices  Part V Appendix  Convergence of sequences of random variables  The essential spectrum of bounded operators  Bibliographical comments
 Control code
 9783319477213
 Dimensions
 unknown
 Extent
 1 online resource (XI, 323 pages)
 File format
 multiple file formats
 Form of item

 online
 electronic
 Governing access note
 Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, noncommercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
 Isbn
 9783319477213
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other control number
 10.1007/9783319477213
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (OCoLC)961117312
 Label
 Random Walks on Reductive Groups, by Yves Benoist, JeanFrançois Quint, (electronic resource)
 Antecedent source
 mixed
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Color
 not applicable
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents
 Introduction  Part I The Law of Large Numbers  Stationary measures  The Law of Large Numbers  Linear random walks  Finite index subsemigroups  Part II Reductive groups  Loxodromic elements  The Jordan projection of semigroups  Reductive groups and their representations  Zariski dense subsemigroups  Random walks on reductive groups  Part III The Central Limit Theorem  Transfer operators over contracting actions  Limit laws for cocycles  Limit laws for products of random matrices  Regularity of the stationary measure  Part IV The Local Limit Theorem  The Spectrum of the complex transfer operator  The Local limit theorem for cocycles  The local limit theorem for products of random matrices  Part V Appendix  Convergence of sequences of random variables  The essential spectrum of bounded operators  Bibliographical comments
 Control code
 9783319477213
 Dimensions
 unknown
 Extent
 1 online resource (XI, 323 pages)
 File format
 multiple file formats
 Form of item

 online
 electronic
 Governing access note
 Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, noncommercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
 Isbn
 9783319477213
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other control number
 10.1007/9783319477213
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (OCoLC)961117312
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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.library.eui.eu/portal/RandomWalksonReductiveGroupsbyYves/VNunwvm92Nc/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.library.eui.eu/portal/RandomWalksonReductiveGroupsbyYves/VNunwvm92Nc/">Random Walks on Reductive Groups, by Yves Benoist, JeanFrançois Quint, (electronic resource)</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.library.eui.eu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.library.eui.eu/">European University Institute</a></span></span></span></span></div>