Heat Kernel Estimates and Law of the Iterated Logarithm for Symmetric Random Walks on Fractal Graphs PDF Download
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Author: Ben M. Hambly
Publisher:
ISBN:
Category : Fractals
Languages : en
Pages : 20
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Book Description
Author: Ben M. Hambly
Publisher:
ISBN:
Category : Fractals
Languages : en
Pages : 20
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Book Description
Author: Alexander Grigor’yan
Publisher: American Mathematical Soc.
ISBN: 147044397X
Category : Mathematics
Languages : en
Pages : 160
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Book Description
A central object of this book is the discrete Laplace operator on finite and infinite graphs. The eigenvalues of the discrete Laplace operator have long been used in graph theory as a convenient tool for understanding the structure of complex graphs. They can also be used in order to estimate the rate of convergence to equilibrium of a random walk (Markov chain) on finite graphs. For infinite graphs, a study of the heat kernel allows to solve the type problem—a problem of deciding whether the random walk is recurrent or transient. This book starts with elementary properties of the eigenvalues on finite graphs, continues with their estimates and applications, and concludes with heat kernel estimates on infinite graphs and their application to the type problem. The book is suitable for beginners in the subject and accessible to undergraduate and graduate students with a background in linear algebra I and analysis I. It is based on a lecture course taught by the author and includes a wide variety of exercises. The book will help the reader to reach a level of understanding sufficient to start pursuing research in this exciting area.
Author: Ben M. Hambly
Publisher:
ISBN:
Category : Fractals
Languages : en
Pages : 26
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Book Description
Abstract: "We examine a class of fractal graphs which arise from a subclass of finitely ramified fractals. The two-sided heat kernel estimates for these graphs are obtained in terms of an effective resistance metric and they are best possible up to constants. If the graph has symmetry, these estimates can be expressed as the usual Gaussian or sub-Gaussian estimates. However, without symmetry, the off-diagonal terms show different decay in different directions. We also discuss the stability of the sub-Gaussian heat kernel estimates under rough isometries."
Author: Motoko Kotani
Publisher: American Mathematical Soc.
ISBN: 0821833510
Category : Mathematics
Languages : en
Pages : 274
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Book Description
Collects papers from the proceedings of the first symposium of the Japan Association for Mathematical Sciences. This book covers topics that center around problems of geometric analysis in relation to heat kernels, random walks, and Poisson boundaries on discrete groups, graphs, and other combinatorial objects.
Author: M. T. Barlow
Publisher: Cambridge University Press
ISBN: 1107674425
Category : Mathematics
Languages : en
Pages : 239
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Book Description
Useful but hard-to-find results enrich this introduction to the analytic study of random walks on infinite graphs.
Author:
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 1608
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Book Description
Author: Pascal Auscher
Publisher: American Mathematical Soc.
ISBN: 0821833839
Category : Mathematics
Languages : en
Pages : 434
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Book Description
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.
Author: M. T. Barlow
Publisher:
ISBN:
Category : Gaussian processes
Languages : en
Pages : 34
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Book Description
Abstract: "Sub-Gaussian estimates for random walks are typical of fractal graphs. We characterize them in the strongly recurrent case, in terms of resistance estimates only, without assuming elliptic Harnac inequalities."
Author: Alexander Grigoryan
Publisher: American Mathematical Soc.
ISBN: 0821849352
Category : Mathematics
Languages : en
Pages : 504
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Book Description
"This volume contains the expanded lecture notes of courses taught at the Emile Borel Centre of the Henri Poincaré 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."--Publisher's website.
Author: Thomas M. Lewis
Publisher:
ISBN:
Category :
Languages : en
Pages : 220
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Book Description
