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Random walks and heat kernels on graphs /
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 Po...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge :
Cambridge University Press,
[2017]
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| Colección: | London Mathematical Society lecture note series ;
438. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 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
- 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
- A.6 Miscellaneous EstimatesA. 7 Whitney Type Coverings of a Ball; A.8 A Maximal Inequality; A.9 Poincaré Inequalities; References; Index