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Author : Zhen-Qing Chen
Publisher :
ISBN 13 : 9781470466381
Total Pages : pages
Book Rating : 4.4/5 (663 download)
Download or read book Stability of Heat Kernel Estimates for Symmetric Non-local Dirichlet Forms written by Zhen-Qing Chen and published by . This book was released on 2021 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Zhen-Qing Chen
Publisher : American Mathematical Society
ISBN 13 : 1470448637
Total Pages : 89 pages
Book Rating : 4.4/5 (74 download)
Download or read book Stability of Heat Kernel Estimates for Symmetric Non-Local Dirichlet Forms written by Zhen-Qing Chen and published by American Mathematical Society. This book was released on 2021-09-24 with total page 89 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.
Author : Zhen-Qing Chen
Publisher : Springer Nature
ISBN 13 : 9811946728
Total Pages : 572 pages
Book Rating : 4.8/5 (119 download)
Download or read book Dirichlet Forms and Related Topics written by Zhen-Qing Chen and published by Springer Nature. This book was released on 2022-09-04 with total page 572 pages. Available in PDF, EPUB and Kindle. Book excerpt: This conference proceeding contains 27 peer-reviewed invited papers from leading experts as well as young researchers all over the world in the related fields that Professor Fukushima has made important contributions to. These 27 papers cover a wide range of topics in probability theory, ranging from Dirichlet form theory, Markov processes, heat kernel estimates, entropy on Wiener spaces, analysis on fractal spaces, random spanning tree and Poissonian loop ensemble, random Riemannian geometry, SLE, space-time partial differential equations of higher order, infinite particle systems, Dyson model, functional inequalities, branching process, to machine learning and Hermitizable problems for complex matrices. Researchers and graduate students interested in these areas will find this book appealing.
Author : Alexander Grigor'yan
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 311070076X
Total Pages : 526 pages
Book Rating : 4.1/5 (17 download)
Download or read book Analysis and Partial Differential Equations on Manifolds, Fractals and Graphs written by Alexander Grigor'yan and published by Walter de Gruyter GmbH & Co KG. This book was released on 2021-01-18 with total page 526 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book covers the latest research in the areas of mathematics that deal the properties of partial differential equations and stochastic processes on spaces in connection with the geometry of the underlying space. Written by experts in the field, this book is a valuable tool for the advanced mathematician.
Author : Jun Kigami
Publisher : American Mathematical Soc.
ISBN 13 : 082185299X
Total Pages : 145 pages
Book Rating : 4.8/5 (218 download)
Download or read book Resistance Forms, Quasisymmetric Maps and Heat Kernel Estimates written by Jun Kigami and published by American Mathematical Soc.. This book was released on 2012-02-22 with total page 145 pages. Available in PDF, EPUB and Kindle. Book excerpt: Assume that there is some analytic structure, a differential equation or a stochastic process for example, on a metric space. To describe asymptotic behaviors of analytic objects, the original metric of the space may not be the best one. Every now and then one can construct a better metric which is somehow ``intrinsic'' with respect to the analytic structure and under which asymptotic behaviors of the analytic objects have nice expressions. The problem is when and how one can find such a metric. In this paper, the author considers the above problem in the case of stochastic processes associated with Dirichlet forms derived from resistance forms. The author's main concerns are the following two problems: (I) When and how to find a metric which is suitable for describing asymptotic behaviors of the heat kernels associated with such processes. (II) What kind of requirement for jumps of a process is necessary to ensure good asymptotic behaviors of the heat kernels associated with such processes.
Author : Andreas Eberle
Publisher : Springer
ISBN 13 : 3319749293
Total Pages : 565 pages
Book Rating : 4.3/5 (197 download)
Download or read book Stochastic Partial Differential Equations and Related Fields written by Andreas Eberle and published by Springer. This book was released on 2018-07-03 with total page 565 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Festschrift contains five research surveys and thirty-four shorter contributions by participants of the conference ''Stochastic Partial Differential Equations and Related Fields'' hosted by the Faculty of Mathematics at Bielefeld University, October 10–14, 2016. The conference, attended by more than 140 participants, including PostDocs and PhD students, was held both to honor Michael Röckner's contributions to the field on the occasion of his 60th birthday and to bring together leading scientists and young researchers to present the current state of the art and promising future developments. Each article introduces a well-described field related to Stochastic Partial Differential Equations and Stochastic Analysis in general. In particular, the longer surveys focus on Dirichlet forms and Potential theory, the analysis of Kolmogorov operators, Fokker–Planck equations in Hilbert spaces, the theory of variational solutions to stochastic partial differential equations, singular stochastic partial differential equations and their applications in mathematical physics, as well as on the theory of regularity structures and paracontrolled distributions. The numerous research surveys make the volume especially useful for graduate students and researchers who wish to start work in the above-mentioned areas, or who want to be informed about the current state of the art.
Author : Janna Ulrike Lierl
Publisher :
ISBN 13 :
Total Pages : 140 pages
Book Rating : 4.:/5 (827 download)
Download or read book Heat Kernel Estimates on Inner Uniform Domains written by Janna Ulrike Lierl and published by . This book was released on 2012 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: We introduce conditions on the symmetric and skew-symmetric parts of timedependent, local, regular forms that imply a parabolic Harnack inequality for appropriate weak solutions of the associated heat equation, under natural assumptions on the underlying space. In particular, these local weak solutions are locally bounded and Holder continuous. Precise two-sided heat kernel estimates are deo rived from this parabolic Harnack inequality. For Dirichlet forms satisfying our conditions we prove a scale-invariant boundary Harnack principle in inner uniform domains. Inner uniformity is a condition on the boundary of the domain that is described solely in terms of the intrinsic length metric of the domain. In addition, we show that the Martin boundary of an inner uniform domain is homeomorphic to the boundary of the domain with respect to its completion in the inner distance. The main result of this work are two-sided Gaussian bounds for Dirichlet heat kernels corresponding to (non- )symmetric, local, regular Dirichlet forms. These bounds hold in domains that satisfy the inner uniformity condition. The proof uses the parabolic Harnack inequality and the boundary Harnack principle described above, as well as the Doob h-transform technique. For inner uniform Euclidean domains, our results apply to divergence form operators that are not necessarily symmetric, and complement earlier results by H. Aikawa, A. Ancona, P. Gyrya, L. Saloff-Coste and K.-T. Sturm.
Author : Pavel Exner
Publisher : American Mathematical Soc.
ISBN 13 : 0821844717
Total Pages : 721 pages
Book Rating : 4.8/5 (218 download)
Download or read book Analysis on Graphs and Its Applications written by Pavel Exner and published by American Mathematical Soc.. This book was released on 2008 with total page 721 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book addresses a new interdisciplinary area emerging on the border between various areas of mathematics, physics, chemistry, nanotechnology, and computer science. The focus here is on problems and techniques related to graphs, quantum graphs, and fractals that parallel those from differential equations, differential geometry, or geometric analysis. Also included are such diverse topics as number theory, geometric group theory, waveguide theory, quantum chaos, quantum wiresystems, carbon nano-structures, metal-insulator transition, computer vision, and communication networks.This volume contains a unique collection of expert reviews on the main directions in analysis on graphs (e.g., on discrete geometric analysis, zeta-functions on graphs, recently emerging connections between the geometric group theory and fractals, quantum graphs, quantum chaos on graphs, modeling waveguide systems and modeling quantum graph systems with waveguides, control theory on graphs), as well as research articles.
Author : Xavier Fernández-Real
Publisher : Springer Nature
ISBN 13 : 3031542428
Total Pages : 409 pages
Book Rating : 4.0/5 (315 download)
Download or read book Integro-Differential Elliptic Equations written by Xavier Fernández-Real and published by Springer Nature. This book was released on 2024 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: Zusammenfassung: This monograph offers a self-contained introduction to the regularity theory for integro-differential elliptic equations, mostly developed in the 21st century. This class of equations finds relevance in fields such as analysis, probability theory, mathematical physics, and in several contexts in the applied sciences. The work gives a detailed presentation of all the necessary techniques, with a primary focus on the main ideas rather than on proving all the results in their greatest generality. The basic building blocks are presented first, with the study of the square root of the Laplacian, and weak solutions to linear equations. Subsequently, the theory of viscosity solutions to nonlinear equations is developed, and proofs are provided for the main known results in this context. The analysis finishes with the investigation of obstacle problems for integro-differential operators and establishes the regularity of solutions and free boundaries. A distinctive feature of this work lies in its presentation of nearly all covered material in a monographic format for the first time, and several proofs streamline, and often simplify, those in the original papers. Furthermore, various open problems are listed throughout the chapters
Author : Jun Kigami
Publisher : American Mathematical Soc.
ISBN 13 : 0821885243
Total Pages : 145 pages
Book Rating : 4.8/5 (218 download)
Download or read book Resistance Forms, Quasisymmetric Maps and Heat Kernel Estimates written by Jun Kigami and published by American Mathematical Soc.. This book was released on 2012 with total page 145 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Hanchao Wang
Publisher :
ISBN 13 :
Total Pages : 15 pages
Book Rating : 4.:/5 (947 download)
Download or read book Heat Kernel Estimates for Markov Processes Associated with Time-dependent Dirichlet Forms written by Hanchao Wang and published by . This book was released on 2015 with total page 15 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, time-inhomogeneous stable-like processes are investigated. We establish the relation between the transition operators and time-dependent parabolic equations, as well as upper heat kernel estimates.
Author : Zhen-qing Chen
Publisher : World Scientific
ISBN 13 : 981459654X
Total Pages : 618 pages
Book Rating : 4.8/5 (145 download)
Download or read book Festschrift Masatoshi Fukushima: In Honor Of Masatoshi Fukushima's Sanju written by Zhen-qing Chen and published by World Scientific. This book was released on 2014-11-27 with total page 618 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains original research papers by leading experts in the fields of probability theory, stochastic analysis, potential theory and mathematical physics. There is also a historical account on Masatoshi Fukushima's contribution to mathematics, as well as authoritative surveys on the state of the art in the field.
Author : Takashi Kumagai
Publisher : Springer
ISBN 13 : 331903152X
Total Pages : 155 pages
Book Rating : 4.3/5 (19 download)
Download or read book Random Walks on Disordered Media and their Scaling Limits written by Takashi Kumagai and published by Springer. This book was released on 2014-01-25 with total page 155 pages. Available in PDF, EPUB and Kindle. Book excerpt: In these lecture notes, we will analyze the behavior of random walk on disordered media by means of both probabilistic and analytic methods, and will study the scaling limits. We will focus on the discrete potential theory and how the theory is effectively used in the analysis of disordered media. The first few chapters of the notes can be used as an introduction to discrete potential theory. Recently, there has been significant progress on the theory of random walk on disordered media such as fractals and random media. Random walk on a percolation cluster(‘the ant in the labyrinth’)is one of the typical examples. In 1986, H. Kesten showed the anomalous behavior of a random walk on a percolation cluster at critical probability. Partly motivated by this work, analysis and diffusion processes on fractals have been developed since the late eighties. As a result, various new methods have been produced to estimate heat kernels on disordered media. These developments are summarized in the notes.
Author : Pascal Auscher
Publisher : American Mathematical Soc.
ISBN 13 : 0821833839
Total Pages : 434 pages
Book Rating : 4.8/5 (218 download)
Download or read book Heat Kernels and Analysis on Manifolds, Graphs, and Metric Spaces written by Pascal Auscher and published by American Mathematical Soc.. This book was released on 2003 with total page 434 pages. 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.
Author : Andreas Weber
Publisher :
ISBN 13 : 9783866441088
Total Pages : 94 pages
Book Rating : 4.4/5 (41 download)
Download or read book Heat Kernel Estimates and L_1hnp Spectral Theory of Locally Symmetric Spaces written by Andreas Weber and published by . This book was released on 2007 with total page 94 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Jay Jorgenson
Publisher : American Mathematical Soc.
ISBN 13 : 0821836986
Total Pages : 410 pages
Book Rating : 4.8/5 (218 download)
Download or read book The Ubiquitous Heat Kernel written by Jay Jorgenson and published by American Mathematical Soc.. This book was released on 2006 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this volume is to bring together research ideas from various fields of mathematics which utilize the heat kernel or heat kernel techniques in their research. The intention of this collection of papers is to broaden productive communication across mathematical sub-disciplines and to provide a vehicle which would allow experts in one field to initiate research with individuals in another field, as well as to give non-experts a resource which can facilitate expanding theirresearch and connecting with others.
Author : Andreas Weber
Publisher :
ISBN 13 :
Total Pages : 23 pages
Book Rating : 4.:/5 (316 download)
Download or read book Heat Kernel Estimates for Locally Symmetric Spaces and the Bottom of the L2-spetrum written by Andreas Weber and published by . This book was released on 2007 with total page 23 pages. Available in PDF, EPUB and Kindle. Book excerpt:
