Introduction to analysis on graphs:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, Rhode Island
AMS American Mathematical Society
[2018]
|
| Schriftenreihe: | University lecture series
volume 71 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | viii, 150 Seiten Illustrationen |
| ISBN: | 9781470443979 |
Internformat
MARC
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| 650 | 4 | |a Finite groups | |
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| 650 | 4 | |a Probability theory and stochastic processes ... Markov processes ... Markov chains (discrete-time Markov processes on discrete state spaces) | |
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Datensatz im Suchindex
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| adam_text | Contents Preface vii Chapter 1. The Laplace operator on graphs 1.1. The notion of a graph 1.2. Cayley graphs 1.3. Random walks 1.4. The Laplace operator 1.5. The Dirichlet problem 1 1 5 8 19 22 Chapter 2. Spectral properties of the Laplace operator 2.1. Green’s formula 2.2. Eigenvalues of the Laplace operator 2.3. Convergence to equilibrium 2.4. More about the eigenvalues 2.5. Convergence to equilibrium for bipartite graphs 2.6. Eigenvalues of Ът 2.7. Products of graphs 2.8. Eigenvalues and mixing time in ZJ^, m odd. 2.9. Eigenvalues and mixing time in a binary cube 27 27 28 34 39 42 43 45 49 51 Chapter 3. Geometric bounds for the eigenvalues 3.1. Cheeger’s inequality 3.2. Eigenvalues on a path graph 3.3. Estimating Ai via diameter 3.4. Expansion rate 53 53 58 61 63 Chapter 4. Eigenvalues on infinite graphs 4.1. Dirichlet Laplace operator 4.2. Cheeger’s inequality 4.3. Isoperimetric and Faber-Krahn inequalities 4.4. Estimating (Ω) via inradius 4.5. Isoperimetric inequalities on Cayley graphs 4.6. Solving the Dirichlet problem by iterations 73 73 76 78 79 82 86 Chapter 5. Estimates of the heat kernel 5.1. The notion and basic properties of the heat kernel 5.2. One-dimensional simple random walk 5.3. Carne-Varopoulos estimate 5.4. On-diagonal upper estimates of the heat kernel 5.5. On-diagonal lower bound via the Dirichlet eigenvalues 5.6. On-diagonal lower bound via volume growth V 89 89 91 96 99 107 112
vi CONTENTS 5.7. Escape rate of random walk 114 Chapter 6. The type problem 6.1. Recurrence and transience 6.2. Recurrence and transience on Cayley graphs 6.3. Volume tests for recurrence 6.4. Isoperimetric tests for transience 117 117 122 123 128 Chapter 7. 131 Exercises Bibliography 143 Index 149
|
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| isbn | 9781470443979 |
| language | English |
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| physical | viii, 150 Seiten Illustrationen |
| publishDate | 2018 |
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| spelling | Grigoryan, Alexander 1957- (DE-588)142557218 aut Introduction to analysis on graphs Alexander Grigor'yan Providence, Rhode Island AMS American Mathematical Society [2018] viii, 150 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier University lecture series volume 71 Combinatorics ... Graph theory ... Graphs and linear algebra (matrices, eigenvalues, etc.) / msc Combinatorics ... Graph theory ... Infinite graphs / msc Combinatorics ... Graph theory ... Graph operations (line graphs, products, etc.) / msc Combinatorics ... Graph theory ... Random walks on graphs / msc Probability theory and stochastic processes ... Markov processes ... Markov chains (discrete-time Markov processes on discrete state spaces) / msc Graph theory Laplace transformation Finite groups Combinatorics ... Graph theory ... Graphs and linear algebra (matrices, eigenvalues, etc.) Combinatorics ... Graph theory ... Infinite graphs Combinatorics ... Graph theory ... Graph operations (line graphs, products, etc.) Combinatorics ... Graph theory ... Random walks on graphs Probability theory and stochastic processes ... Markov processes ... Markov chains (discrete-time Markov processes on discrete state spaces) Lokal endlicher Graph (DE-588)4844040-1 gnd rswk-swf Analysis (DE-588)4001865-9 gnd rswk-swf Laplace-Operator (DE-588)4166772-4 gnd rswk-swf Lokal endlicher Graph (DE-588)4844040-1 s Analysis (DE-588)4001865-9 s Laplace-Operator (DE-588)4166772-4 s DE-604 Erscheint auch als Online-Ausgabe 978-1-4704-4855-4 University lecture series volume 71 (DE-604)BV004153846 71 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030550028&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Grigoryan, Alexander 1957- Introduction to analysis on graphs University lecture series Combinatorics ... Graph theory ... Graphs and linear algebra (matrices, eigenvalues, etc.) / msc Combinatorics ... Graph theory ... Infinite graphs / msc Combinatorics ... Graph theory ... Graph operations (line graphs, products, etc.) / msc Combinatorics ... Graph theory ... Random walks on graphs / msc Probability theory and stochastic processes ... Markov processes ... Markov chains (discrete-time Markov processes on discrete state spaces) / msc Graph theory Laplace transformation Finite groups Combinatorics ... Graph theory ... Graphs and linear algebra (matrices, eigenvalues, etc.) Combinatorics ... Graph theory ... Infinite graphs Combinatorics ... Graph theory ... Graph operations (line graphs, products, etc.) Combinatorics ... Graph theory ... Random walks on graphs Probability theory and stochastic processes ... Markov processes ... Markov chains (discrete-time Markov processes on discrete state spaces) Lokal endlicher Graph (DE-588)4844040-1 gnd Analysis (DE-588)4001865-9 gnd Laplace-Operator (DE-588)4166772-4 gnd |
| subject_GND | (DE-588)4844040-1 (DE-588)4001865-9 (DE-588)4166772-4 |
| title | Introduction to analysis on graphs |
| title_auth | Introduction to analysis on graphs |
| title_exact_search | Introduction to analysis on graphs |
| title_full | Introduction to analysis on graphs Alexander Grigor'yan |
| title_fullStr | Introduction to analysis on graphs Alexander Grigor'yan |
| title_full_unstemmed | Introduction to analysis on graphs Alexander Grigor'yan |
| title_short | Introduction to analysis on graphs |
| title_sort | introduction to analysis on graphs |
| topic | Combinatorics ... Graph theory ... Graphs and linear algebra (matrices, eigenvalues, etc.) / msc Combinatorics ... Graph theory ... Infinite graphs / msc Combinatorics ... Graph theory ... Graph operations (line graphs, products, etc.) / msc Combinatorics ... Graph theory ... Random walks on graphs / msc Probability theory and stochastic processes ... Markov processes ... Markov chains (discrete-time Markov processes on discrete state spaces) / msc Graph theory Laplace transformation Finite groups Combinatorics ... Graph theory ... Graphs and linear algebra (matrices, eigenvalues, etc.) Combinatorics ... Graph theory ... Infinite graphs Combinatorics ... Graph theory ... Graph operations (line graphs, products, etc.) Combinatorics ... Graph theory ... Random walks on graphs Probability theory and stochastic processes ... Markov processes ... Markov chains (discrete-time Markov processes on discrete state spaces) Lokal endlicher Graph (DE-588)4844040-1 gnd Analysis (DE-588)4001865-9 gnd Laplace-Operator (DE-588)4166772-4 gnd |
| topic_facet | Combinatorics ... Graph theory ... Graphs and linear algebra (matrices, eigenvalues, etc.) / msc Combinatorics ... Graph theory ... Infinite graphs / msc Combinatorics ... Graph theory ... Graph operations (line graphs, products, etc.) / msc Combinatorics ... Graph theory ... Random walks on graphs / msc Probability theory and stochastic processes ... Markov processes ... Markov chains (discrete-time Markov processes on discrete state spaces) / msc Graph theory Laplace transformation Finite groups Combinatorics ... Graph theory ... Graphs and linear algebra (matrices, eigenvalues, etc.) Combinatorics ... Graph theory ... Infinite graphs Combinatorics ... Graph theory ... Graph operations (line graphs, products, etc.) Combinatorics ... Graph theory ... Random walks on graphs Probability theory and stochastic processes ... Markov processes ... Markov chains (discrete-time Markov processes on discrete state spaces) Lokal endlicher Graph Analysis Laplace-Operator |
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