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Random Walks and Heat Kernels on Graphs

2017-02-23 Mathematics
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Release : 2017-02-23
Genre : Mathematics
Kind : eBook
Book Rating : 593/5 ( reviews)

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Book Synopsis Random Walks and Heat Kernels on Graphs by : Martin T. Barlow

Download or read book Random Walks and Heat Kernels on Graphs written by Martin T. Barlow. This book was released on 2017-02-23. Available in PDF, EPUB and Kindle. Book excerpt: 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 Poincaré 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.

Random Walks and Heat Kernels on Graphs

2017-02-23 Mathematics
Download Random Walks and Heat Kernels on Graphs PDF Online Free

Author :
Release : 2017-02-23
Genre : Mathematics
Kind : eBook
Book Rating : 425/5 ( reviews)

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Book Synopsis Random Walks and Heat Kernels on Graphs by : M. T. Barlow

Download or read book Random Walks and Heat Kernels on Graphs written by M. T. Barlow. This book was released on 2017-02-23. Available in PDF, EPUB and Kindle. Book excerpt: Useful but hard-to-find results enrich this introduction to the analytic study of random walks on infinite graphs.

Heat Kernels and Analysis on Manifolds, Graphs, and Metric Spaces

2003 Mathematics
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Release : 2003
Genre : Mathematics
Kind : eBook
Book Rating : 839/5 ( reviews)

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Book Synopsis Heat Kernels and Analysis on Manifolds, Graphs, and Metric Spaces by : Pascal Auscher

Download or read book Heat Kernels and Analysis on Manifolds, Graphs, and Metric Spaces written by Pascal Auscher. This book was released on 2003. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the expanded lecture notes of courses taught at the Emile Borel Centre of the Henri Poincare Institute (Paris). In the book, leading experts introduce recent research in their fields. The unifying theme is the study of heat kernels in various situations using related geometric and analytic tools. Topics include analysis of complex-coefficient elliptic operators, diffusions on fractals and on infinite-dimensional groups, heat kernel and isoperimetry on Riemannian manifolds, heat kernels and infinite dimensional analysis, diffusions and Sobolev-type spaces on metric spaces, quasi-regular mappings and $p$-Laplace operators, heat kernel and spherical inversion on $SL 2(C)$, random walks and spectral geometry on crystal lattices, isoperimetric and isocapacitary inequalities, and generating function techniques for random walks on graphs. This volume is suitable for graduate students and research mathematicians interested in random processes and analysis on manifolds.

Heat Kernel Estimates and Law of the Iterated Logarithm for Symmetric Random Walks on Fractal Graphs

2003 Fractals
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Release : 2003
Genre : Fractals
Kind : eBook
Book Rating : /5 ( reviews)

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Book Synopsis Heat Kernel Estimates and Law of the Iterated Logarithm for Symmetric Random Walks on Fractal Graphs by : Ben M. Hambly

Download or read book Heat Kernel Estimates and Law of the Iterated Logarithm for Symmetric Random Walks on Fractal Graphs written by Ben M. Hambly. This book was released on 2003. Available in PDF, EPUB and Kindle. Book excerpt:

The Art of Random Walks

2006-05-17 Mathematics
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Release : 2006-05-17
Genre : Mathematics
Kind : eBook
Book Rating : 275/5 ( reviews)

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Book Synopsis The Art of Random Walks by : Andras Telcs

Download or read book The Art of Random Walks written by Andras Telcs. This book was released on 2006-05-17. Available in PDF, EPUB and Kindle. Book excerpt: Einstein proved that the mean square displacement of Brownian motion is proportional to time. He also proved that the diffusion constant depends on the mass and on the conductivity (sometimes referred to Einstein’s relation). The main aim of this book is to reveal similar connections between the physical and geometric properties of space and diffusion. This is done in the context of random walks in the absence of algebraic structure, local or global spatial symmetry or self-similarity. The author studies the heat diffusion at this general level and discusses the following topics: The multiplicative Einstein relation, Isoperimetric inequalities, Heat kernel estimates Elliptic and parabolic Harnack inequality.

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