Discrete Probability Models and Methods Probability on Graphs and Tr
The emphasis in this book is placed on general models (Markov chains, random fields, random graphs), universal methods (the probabilistic method, the coupling method, the Stein-Chen method, martingale methods, the method of types) and versatile tools (Che
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Pierre Brémaud
Discrete Probability Models and Methods Probability on Graphs and Trees, Markov Chains and Random Fields, Entropy and Coding
Probability Theory and Stochastic Modelling Volume 78
Editors-in-chief Søren Asmussen, Aarhus, Denmark Peter W. Glynn, Stanford, CA, USA Yves Le Jan, Orsay, France Advisory Board Martin Hairer, Coventry, UK Peter Jagers, Gothenburg, Sweden Ioannis Karatzas, New York, NY, USA Frank P. Kelly, Cambridge, UK Andreas E. Kyprianou, Bath, UK Bernt Øksendal, Oslo, Norway George Papanicolaou, Stanford, CA, USA Etienne Pardoux, Marseille, France Edwin Perkins, Vancouver, BC, Canada Halil Mete Soner, Zürich, Switzerland
The Probability Theory and Stochastic Modelling series is a merger and continuation of Springer’s two well established series Stochastic Modelling and Applied Probability and Probability and Its Applications series. It publishes research monographs that make a significant contribution to probability theory or an applications domain in which advanced probability methods are fundamental. Books in this series are expected to follow rigorous mathematical standards, while also displaying the expository quality necessary to make them useful and accessible to advanced students as well as researchers. The series covers all aspects of modern probability theory including • • • • • •
Gaussian processes Markov processes Random fields, point processes and random sets Random matrices Statistical mechanics and random media Stochastic analysis
as well as applications that include (but are not restricted to): • Branching processes and other models of population growth • Communications and processing networks • Computational methods in probability and stochastic processes, including simulation • Genetics and other stochastic models in biology and the life sciences • Information theory, signal processing, and image synthesis • Mathematical economics and finance • Statistical methods (e.g. empirical processes, MCMC) • Statistics for stochastic processes • Stochastic control • Stochastic models in operations research and stochastic optimization • Stochastic models in the physical sciences
More information about this series at http://www.springer.com/series/13205
Pierre Brémaud
Discrete Probability Models and Methods Probability on Graphs and Trees, Markov Chains and Random Fields, Entropy and Coding
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Pierre Brémaud École Polytechnique Fédérale de Lausanne (EPFL) Lausanne Switzerland
ISSN 2199-3130 ISSN 2199-3149 (electronic) Probability Theory and Stochastic Modelling ISBN 978-3-319-43475-9 ISBN 978-3-319-43476-6 (eBook) DOI 10.1007/978-3-319-43476-6 Library of Congress Control Number: 2016962040 Mathematics Subject Classification (2010): 60J10, 68Q87, 68W20, 68W40, 05C80, 05C81, 60G60, 60G42, 60C05, 60K05, 60J80, 60K15 © Springer International Publishing Switzerland 2017 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, re
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