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Titlebook: Scaling Limits of Interacting Particle Systems; Claude Kipnis,Claudio Landim Book 1999 Springer-Verlag Berlin Heidelberg 1999 Dirichlet fo

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書目名稱Scaling Limits of Interacting Particle Systems
編輯Claude Kipnis,Claudio Landim
視頻videohttp://file.papertrans.cn/862/861108/861108.mp4
概述This book is long-awaited in the "interacting particle systems" community..Begun by Claude Kipnis before his untimely death, it was completed by Claudio Landim, his most brilliant student and collabor
叢書名稱Grundlehren der mathematischen Wissenschaften
圖書封面Titlebook: Scaling Limits of Interacting Particle Systems;  Claude Kipnis,Claudio Landim Book 1999 Springer-Verlag Berlin Heidelberg 1999 Dirichlet fo
描述The idea of writing up a book on the hydrodynamic behavior of interacting particle systems was born after a series of lectures Claude Kipnis gave at the University of Paris 7 in the spring of 1988. At this time Claude wrote some notes in French that covered Chapters 1 and 4, parts of Chapters 2, 5 and Appendix 1 of this book. His intention was to prepare a text that was as self-contained as possible. lt would include, for instance, all tools from Markov process theory ( cf. Appendix 1, Chaps. 2 and 4) necessary to enable mathematicians and mathematical physicists with some knowledge of probability, at the Ievel of Chung (1974), to understand the techniques of the theory of hydrodynamic Iimits of interacting particle systems. In the fall of 1991 Claude invited me to complete his notes with him and transform them into a book that would present to a large audience the latest developments of the theory in a simple and accessible form. To concentrate on the main ideas and to avoid unnecessary technical difficulties, we decided to consider systems evolving in finite lattice spaces and for which the equilibrium states are product measures. To illustrate the techniques we chose two well-kn
出版日期Book 1999
關(guān)鍵詞Dirichlet form; Feynman-Kac formula; Hydrodynamic Limits; Interacting Particle Systems; Markov chain; Mar
版次1
doihttps://doi.org/10.1007/978-3-662-03752-2
isbn_softcover978-3-642-08444-7
isbn_ebook978-3-662-03752-2Series ISSN 0072-7830 Series E-ISSN 2196-9701
issn_series 0072-7830
copyrightSpringer-Verlag Berlin Heidelberg 1999
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Weak Formulations of Local Equilibrium,conservation of local equilibrium. Unfortunately, at the present state of knowledge, there is no satisfactory general proof of conservation of local equilibrium for large classes of interacting particle systems. All existing approaches to this problem rely too much on particular features of the mode
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An Example of Reversible Gradient System: Symmetric Zero Range Processes,or technical difficulties, we consider the simplest prototype of reversible gradient system: the nearest neighbor symmetric zero range process. The generator of this Markov process is given by.for cylinder functions .: ?T.→?.
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Hydrodynamic Limit of Asymmetric Attractive Processes,advantage over the one presented in Chapter 6 that it does not require the solution of the hydrodynamic equation to be smooth. On the other hand its main inconvenience is that it assumes the process to be attractive to permit the use of coupling arguments and the initial state to be a product measur
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