Harmonic Functions And Potentials On Finite Or Infinite Networks

Author : Victor Anandam
Publisher : Springer Science & Business Media
Page : 152 pages
File Size : 44,9 Mb
Release : 2011-06-27
Category : Mathematics
ISBN : 9783642213991

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Harmonic Functions and Potentials on Finite or Infinite Networks by Victor Anandam Pdf

Random walks, Markov chains and electrical networks serve as an introduction to the study of real-valued functions on finite or infinite graphs, with appropriate interpretations using probability theory and current-voltage laws. The relation between this type of function theory and the (Newton) potential theory on the Euclidean spaces is well-established. The latter theory has been variously generalized, one example being the axiomatic potential theory on locally compact spaces developed by Brelot, with later ramifications from Bauer, Constantinescu and Cornea. A network is a graph with edge-weights that need not be symmetric. This book presents an autonomous theory of harmonic functions and potentials defined on a finite or infinite network, on the lines of axiomatic potential theory. Random walks and electrical networks are important sources for the advancement of the theory.

Author : Paolo M. Soardi
Publisher : Springer
Page : 199 pages
File Size : 41,5 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540487982

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Potential Theory on Infinite Networks by Paolo M. Soardi Pdf

The aim of the book is to give a unified approach to new developments in discrete potential theory and infinite network theory. The author confines himself to the finite energy case, but this does not result in loss of complexity. On the contrary, the functional analytic machinery may be used in analogy with potential theory on Riemann manifolds. The book is intended for researchers with interdisciplinary interests in one of the following fields: Markov chains, combinatorial graph theory, network theory, Dirichlet spaces, potential theory, abstract harmonic analysis, theory of boundaries.

Author : Palle Jorgensen,Erin P J Pearse
Publisher : World Scientific
Page : 449 pages
File Size : 45,8 Mb
Release : 2023-03-21
Category : Mathematics
ISBN : 9789811265532

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Operator Theory And Analysis Of Infinite Networks by Palle Jorgensen,Erin P J Pearse Pdf

This volume considers resistance networks: large graphs which are connected, undirected, and weighted. Such networks provide a discrete model for physical processes in inhomogeneous media, including heat flow through perforated or porous media. These graphs also arise in data science, e.g., considering geometrizations of datasets, statistical inference, or the propagation of memes through social networks. Indeed, network analysis plays a crucial role in many other areas of data science and engineering. In these models, the weights on the edges may be understood as conductances, or as a measure of similarity. Resistance networks also arise in probability, as they correspond to a broad class of Markov chains.The present volume takes the nonstandard approach of analyzing resistance networks from the point of view of Hilbert space theory, where the inner product is defined in terms of Dirichlet energy. The resulting viewpoint emphasizes orthogonality over convexity and provides new insights into the connections between harmonic functions, operators, and boundary theory. Novel applications to mathematical physics are given, especially in regard to the question of self-adjointness of unbounded operators.New topics are covered in a host of areas accessible to multiple audiences, at both beginning and more advanced levels. This is accomplished by directly linking diverse applied questions to such key areas of mathematics as functional analysis, operator theory, harmonic analysis, optimization, approximation theory, and probability theory.

Author : Nalini Anantharaman,Ashkan Nikeghbali,Michael Th. Rassias
Publisher : Springer Nature
Page : 449 pages
File Size : 44,7 Mb
Release : 2020-11-21
Category : Mathematics
ISBN : 9783030564094

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Frontiers in Analysis and Probability by Nalini Anantharaman,Ashkan Nikeghbali,Michael Th. Rassias Pdf

The volume presents extensive research devoted to a broad spectrum of mathematical analysis and probability theory. Subjects discussed in this Work are those treated in the so-called Strasbourg–Zürich Meetings. These meetings occur twice yearly in each of the cities, Strasbourg and Zürich, venues of vibrant mathematical communication and worldwide gatherings. The topical scope of the book includes the study of monochromatic random waves defined for general Riemannian manifolds, notions of entropy related to a compact manifold of negative curvature, interacting electrons in a random background, lp-cohomology (in degree one) of a graph and its connections with other topics, limit operators for circular ensembles, polyharmonic functions for finite graphs and Markov chains, the ETH-Approach to Quantum Mechanics, 2-dimensional quantum Yang–Mills theory, Gibbs measures of nonlinear Schrödinger equations, interfaces in spectral asymptotics and nodal sets. Contributions in this Work are composed by experts from the international community, who have presented the state-of-the-art research in the corresponding problems treated. This volume is expected to be a valuable resource to both graduate students and research mathematicians working in analysis, probability as well as their interconnections and applications.

Author : Paolo Maurizio Soardi
Publisher : Springer Verlag
Page : 187 pages
File Size : 43,8 Mb
Release : 1994-01-01
Category : Mathematics
ISBN : OCLC:36786229

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Potential Theory on Infinite Networks by Paolo Maurizio Soardi Pdf

The aim of the book is to give a unified approach to new developments in discrete potential theory and infinite network theory. The author confines himself to the finite energy case, but this does not result in loss of complexity. On the contrary, the functional analytic machinery may be used in analogy with potential theory on Riemann manifolds.The book is intended for researchers with interdisciplinary interests in one of the following fields: Markov chains, combinatorial graph theory, network theory, Dirichlet spaces, potential theory, abstract harmonic analysis, theory of boundaries.

Author : Andre Boivin,Javad Mashreghi
Publisher : American Mathematical Soc.
Page : 347 pages
File Size : 44,5 Mb
Release : 2012
Category : Mathematics
ISBN : 9780821891735

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Complex Analysis and Potential Theory by Andre Boivin,Javad Mashreghi Pdf

This is the proceedings volume of an international conference entitled Complex Analysis and Potential Theory, which was held to honor the important contributions of two influential analysts, Kohur N. GowriSankaran and Paul M. Gauthier, in June 2011 at the Centre de Recherches Mathematiques (CRM) in Montreal. More than fifty mathematicians from fifteen countries participated in the conference. The twenty-four surveys and research articles contained in this book are based on the lectures given by some of the most established specialists in the fields. They reflect the wide breadth of research interests of the two honorees: from potential theory on trees to approximation on Riemann surfaces, from universality to inner and outer functions and the disc algebra, from branching processes to harmonic extension and capacities, from harmonic mappings and the Harnack principle to integration formulae in $\mathbb {C}^n$ and the Hartogs phenomenon, from fine harmonicity and plurisubharmonic functions to the binomial identity and the Riemann hypothesis, and more. This volume will be a valuable resource for specialists, young researchers, and graduate students from both fields, complex analysis and potential theory. It will foster further cooperation and the exchange of ideas and techniques to find new research perspectives.

Author : Matthias Keller,Daniel Lenz,Radosław K. Wojciechowski
Publisher : Springer Nature
Page : 675 pages
File Size : 40,9 Mb
Release : 2021-10-22
Category : Mathematics
ISBN : 9783030814595

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Graphs and Discrete Dirichlet Spaces by Matthias Keller,Daniel Lenz,Radosław K. Wojciechowski Pdf

The spectral geometry of infinite graphs deals with three major themes and their interplay: the spectral theory of the Laplacian, the geometry of the underlying graph, and the heat flow with its probabilistic aspects. In this book, all three themes are brought together coherently under the perspective of Dirichlet forms, providing a powerful and unified approach. The book gives a complete account of key topics of infinite graphs, such as essential self-adjointness, Markov uniqueness, spectral estimates, recurrence, and stochastic completeness. A major feature of the book is the use of intrinsic metrics to capture the geometry of graphs. As for manifolds, Dirichlet forms in the graph setting offer a structural understanding of the interaction between spectral theory, geometry and probability. For graphs, however, the presentation is much more accessible and inviting thanks to the discreteness of the underlying space, laying bare the main concepts while preserving the deep insights of the manifold case. Graphs and Discrete Dirichlet Spaces offers a comprehensive treatment of the spectral geometry of graphs, from the very basics to deep and thorough explorations of advanced topics. With modest prerequisites, the book can serve as a basis for a number of topics courses, starting at the undergraduate level.

Author : T.T Chelvam
Publisher : ALPHA SCIENCE INTERNATIONAL LIMITED
Page : 370 pages
File Size : 42,7 Mb
Release : 2009-12-03
Category : Mathematics
ISBN : 9788184873108

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Algebra, Graph Theory and their Applications by T.T Chelvam Pdf

Algebra and Graph Theory are two fascinating branches of Mathematics. The tools of each have been used in the other to explore and investigate problems in depth. Especially the Cayley graphs constructed out of the group structures have been greatly and extensively used in Parallel computers to provide network to the routing problem. ALGEBRA, GRAPH THEORY AND THEIR APPLICATIONS takes an inclusive view of the two areas and presents a wide range of topics. It includes sixteen referred research articles on algebra and graph theory of which three are expository in nature alongwith articles exhibiting the use of algebraic techniques in the study of graphs. A substantial proportion of the book covers topics that have not yet appeared in book form providing a useful resource to the younger generation of researchers in Discrete Mathematics.

Author : Anonim
Publisher : Unknown
Page : 486 pages
File Size : 49,9 Mb
Release : 2015
Category : Mathematics
ISBN : IND:30000153092204

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Hokkaido Mathematical Journal by Anonim Pdf

Author : M. Picardello,W. Woess
Publisher : Cambridge University Press
Page : 378 pages
File Size : 49,8 Mb
Release : 1999-11-18
Category : Mathematics
ISBN : 0521773121

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Random Walks and Discrete Potential Theory by M. Picardello,W. Woess Pdf

Comprehensive and interdisciplinary text covering the interplay between random walks and structure theory.

Author : M. T. Barlow
Publisher : Cambridge University Press
Page : 239 pages
File Size : 40,9 Mb
Release : 2017-02-23
Category : Mathematics
ISBN : 9781107674424

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Random Walks and Heat Kernels on Graphs by M. T. Barlow Pdf

Useful but hard-to-find results enrich this introduction to the analytic study of random walks on infinite graphs.

Author : David J. Aldous,James Propp
Publisher : American Mathematical Soc.
Page : 240 pages
File Size : 55,6 Mb
Release : 1998-01-01
Category : Mathematics
ISBN : 0821870858

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Microsurveys in Discrete Probability by David J. Aldous,James Propp Pdf

This book contains eleven articles surveying emerging topics in discrete probability. The papers are based on talks given by experts at the DIMACS "Microsurveys in Discrete Probability" workshop held at the Institute for Advanced Study, Princeton, NJ, in 1997. This compilation of current research in discrete probability provides a unique overview that is not available elsewhere in book or survey form. Topics covered in the volume include: Markov chains (pefect sampling, coupling from the past, mixing times), random trees (spanning trees on infinite graphs, enumeration of trees and forests, tree-valued Markov chains), distributional estimates (method of bounded differences, Stein-Chen method for normal approximation), dynamical percolation, Poisson processes, and reconstructing random walk from scenery.

Author : Anonim
Publisher : Unknown
Page : 746 pages
File Size : 46,7 Mb
Release : 1989
Category : Functions of complex variables
ISBN : UOM:39015015473930

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Reviews in Complex Analysis, 1980-86 by Anonim Pdf

Author : Daniel Lenz,Florian Sobieczky,Wolfgang Woess
Publisher : Springer Science & Business Media
Page : 345 pages
File Size : 54,6 Mb
Release : 2011-06-16
Category : Mathematics
ISBN : 9783034602440

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Random Walks, Boundaries and Spectra by Daniel Lenz,Florian Sobieczky,Wolfgang Woess Pdf

These proceedings represent the current state of research on the topics 'boundary theory' and 'spectral and probability theory' of random walks on infinite graphs. They are the result of the two workshops held in Styria (Graz and St. Kathrein am Offenegg, Austria) between June 29th and July 5th, 2009. Many of the participants joined both meetings. Even though the perspectives range from very different fields of mathematics, they all contribute with important results to the same wonderful topic from structure theory, which, by extending a quotation of Laurent Saloff-Coste, could be described by 'exploration of groups by random processes'.

Author : Józef Dodziuk,Linda Keen
Publisher : American Mathematical Soc.
Page : 490 pages
File Size : 53,7 Mb
Release : 1997
Category : Mathematics
ISBN : 9780821806715

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Lipa's Legacy by Józef Dodziuk,Linda Keen Pdf

The mathematical works of Lars Ahlfors and Lipman Bers are fundamental and lasting. They have influenced and altered the development of twentieth century mathematics. The personalities of these two scientists helped create a mathematical family and have had a permanent positive effect on a whole generation of mathematicians. Their mathematical heritage continues to lead succeeding generations. In the fall of 1994, one year after Bers' death, some members of this family decided to inaugurate a series of conferences, "The Bers Colloquium", to be held every three years. The theme was to be a topic in the Ahlfors-Bers mathematical tradition, broadly interpreted. Ahlfors died a year after the first colloquium; future colloquia in this series will be called "The Ahlfors-Bers Colloquium". The first colloquium was held in October 1995 at the Graduate Center, CUNY in New York. It coincided roughly with the second anniversary of Ber's death. There were six lectures and much informal mathematical discussion. This volume contains papers by the speakers and many of the participants. The broad range of papers indicate how strong and far reaching Ber's influence has been. The topics represented in the book include Teichmuller theory, Kleinian groups, higher dimensional hyperbolic geometry, geometry of numbers, circle packings, theory of discrete groups, classical complex function theory, one dimensional dynamics, fluid dynamics, quasiconformal mappings in higher dimensions, partial differential equations, and classical algebraic geometry. partial