Random walks and heat kernels on graphs /
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| Author / Creator: | Barlow, M. T. |
|---|---|
| Imprint: | ©2017 Cambridge : Cambridge University Press, [2017] |
| Description: | 1 online resource |
| Language: | English |
| Series: | London Mathematical Society lecture note series ; 438 London Mathematical Society lecture note series ; 438. |
| Subject: | |
| Format: | E-Resource Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/13454746 |
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| 100 | 1 | |a Barlow, M. T. | |
| 245 | 1 | 0 | |a Random walks and heat kernels on graphs / |c Martin T. Barlow, University of British Columbia, Canada. |
| 264 | 4 | |c ©2017 | |
| 264 | 1 | |a Cambridge : |b Cambridge University Press, |c [2017] | |
| 300 | |a 1 online resource | ||
| 336 | |a text |b txt |2 rdacontent | ||
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| 490 | 1 | |a London Mathematical Society lecture note series ; |v 438 | |
| 504 | |a Includes bibliographical references and index. | ||
| 588 | 0 | |a Print version record. | |
| 505 | 0 | |a Cover; Series page; Title page; Copyright page; Dedication; Contents; Preface; 1 Introduction; 1.1 Graphs and Weighted Graphs; 1.2 Random Walks on a Weighted Graph; 1.3 Transition Densities and the Laplacian; 1.4 Dirichlet or Energy Form; 1.5 Killed Process; 1.6 Green's Functions; 1.7 Harmonic Functions, Harnack Inequalities, and the Liouville Property; 1.8 Strong Liouville Property for R[sup(d)]; 1.9 Interpretation of the Liouville Property; 2 Random Walks and Electrical Resistance; 2.1 Basic Concepts; 2.2 Transience and Recurrence; 2.3 Energy and Variational Methods | |
| 505 | 8 | |a 2.4 Resistance to Infinity2.5 Traces and Electrical Equivalence; 2.6 Stability under Rough Isometries; 2.7 Hitting Times and Resistance; 2.8 Examples; 2.9 The Sierpinski Gasket Graph; 3 Isoperimetric Inequalities and Applications; 3.1 Isoperimetric Inequalities; 3.2 Nash Inequality; 3.3 Poincaré Inequality; 3.4 Spectral Decomposition for a Finite Graph; 3.5 Strong Isoperimetric Inequality and Spectral Radius; 4 Discrete Time Heat Kernel; 4.1 Basic Properties and Bounds on the Diagonal; 4.2 Carne-Varopoulos Bound; 4.3 Gaussian and Sub-Gaussian Heat Kernel Bounds; 4.4 Off-diagonal Upper Bounds | |
| 505 | 8 | |a A.6 Miscellaneous EstimatesA. 7 Whitney Type Coverings of a Ball; A.8 A Maximal Inequality; A.9 Poincaré Inequalities; References; Index | |
| 520 | |a This introduction to random walks on infinite graphs gives particular emphasis to graphs with polynomial volume growth. It offers an overview of analytic methods, starting with the connection between random walks and electrical resistance, and then proceeding to study the use of isoperimetric and Poincar inequalities. The book presents rough isometries and looks at the properties of a graph that are stable under these transformations. Applications include the 'type problem': determining whether a graph is transient or recurrent. The final chapters show how geometric properties of the graph can be used to establish heat kernel bounds, that is, bounds on the transition probabilities of the random walk, and it is proved that Gaussian bounds hold for graphs that are roughly isometric to Euclidean space. Aimed at graduate students in mathematics, the book is also useful for researchers as a reference for results that are hard to find elsewhere. | ||
| 650 | 0 | |a Random walks (Mathematics) |0 http://id.loc.gov/authorities/subjects/sh85111357 | |
| 650 | 0 | |a Graph theory. |0 http://id.loc.gov/authorities/subjects/sh85056471 | |
| 650 | 0 | |a Markov processes. |0 http://id.loc.gov/authorities/subjects/sh85081369 | |
| 650 | 0 | |a Heat equation. |0 http://id.loc.gov/authorities/subjects/sh85059782 | |
| 650 | 0 | |a Mathematics. |0 http://id.loc.gov/authorities/subjects/sh85082139 | |
| 650 | 1 | 2 | |a Markov Chains |
| 650 | 1 | 2 | |a Mathematics |
| 650 | 6 | |a Marches aléatoires (Mathématiques) | |
| 650 | 6 | |a Processus de Markov. | |
| 650 | 6 | |a Équation de la chaleur. | |
| 650 | 6 | |a Mathématiques. | |
| 650 | 7 | |a MATHEMATICS |x General. |2 bisacsh | |
| 650 | 7 | |a Graph theory. |2 fast |0 (OCoLC)fst00946584 | |
| 650 | 7 | |a Heat equation. |2 fast |0 (OCoLC)fst00953865 | |
| 650 | 7 | |a Markov processes. |2 fast |0 (OCoLC)fst01010347 | |
| 650 | 7 | |a Random walks (Mathematics) |2 fast |0 (OCoLC)fst01089818 | |
| 655 | 4 | |a Electronic books. | |
| 776 | 0 | 8 | |i Print version: |a Barlow, M.T. |t Random walks and heat kernels on graphs. |d Cambridge : Cambridge University Press, [2017] |z 9781107674424 |w (DLC) 2016051295 |w (OCoLC)958098175 |
| 830 | 0 | |a London Mathematical Society lecture note series ; |v 438. | |
| 856 | 4 | 0 | |u https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=e000xna&AN=1458586 |y eBooks on EBSCOhost |
| 880 | 8 | |6 505-00/(S |a 4.5 Lower Bounds5 Continuous Time Random Walks; 5.1 Introduction to Continuous Time; 5.2 Heat Kernel Bounds; 6 Heat Kernel Bounds; 6.1 Strongly Recurrent Graphs; 6.2 Gaussian Upper Bounds; 6.3 Poincaré Inequality and Gaussian Lower Bounds; 6.4 Remarks on Gaussian Bounds; 7 Potential Theory and Harnack Inequalities; 7.1 Introduction to Potential Theory; 7.2 Applications; Appendix; A.1 Martingales and Tail Estimates; A.2 Discrete Time Markov Chains and the Strong Markov Property; A.3 Continuous Time Random Walk; A.4 Invariant and Tail σ-fields; A.5 Hilbert Space Results | |
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| 928 | |t Library of Congress classification |a QA274.73.B3735 2017eb |l Online |c UC-FullText |u https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=e000xna&AN=1458586 |z eBooks on EBSCOhost |g ebooks |i 13596410 | ||