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＜電子ブック＞
A course on large deviations with an introduction to Gibbs measures / Firas Rassoul-Agha, Timo Sepp�al�ainen
(Graduate Studies in Mathematics ; v. 162)

出版者	(Providence, Rhode Island : American Mathematical Society)
出版年	2015
大きさ	1 online resource (xiv, 318 pages)
著者標目	*Rassoul-Agha, Firas Sepp�al�ainen, Timo O
件　名	LCSH:Large deviations LCSH:Probabilities LCSH:Measure theory FREE:Probability theory and stochastic processes -- Instructional exposition (textbooks, tutorial papers, etc.)  全ての件名で検索 FREE:Probability theory and stochastic processes -- Limit theorems -- Large deviations  全ての件名で検索 FREE:Probability theory and stochastic processes -- Markov processes -- Markov chains (discrete-time Markov processes on discrete state spaces)  全ての件名で検索 FREE:Probability theory and stochastic processes -- Special processes -- Interacting random processes; statistical mechanics type models; percolation theory  全ての件名で検索 FREE:Probability theory and stochastic processes -- Special processes -- Processes in random environments  全ての件名で検索 FREE:Statistical mechanics, structure of matter -- Equilibrium statistical mechanics -- Classical equilibrium statistical mechanics (general)  全ての件名で検索 FREE:Statistical mechanics, structure of matter -- Equilibrium statistical mechanics -- Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs  全ての件名で検索
内容注記	Chapter 1. Introductory discussion Chapter 2. The large deviation principle Chapter 3. Large deviations and asymptotics of integrals Chapter 4. Convex analysis in large deviation theory Chapter 5. Relative entropy and large deviations for empirical measures Chapter 6. Process level large deviations for i.i.d. fields Chapter 7. Formalism for classical lattice systems Chapter 8. Large deviations and equilibrium statistical mechanics Chapter 9. Phase transition in the Ising model Chapter 10. Percolation approach to phase transition Chapter 11. Further asymptotics for i.i.d. random variables Chapter 12. Large deviations through the limiting generating function Chapter 13. Large deviations for Markov chains Chapter 14. Convexity criterion for large deviations Chapter 15. Nonstationary independent variables Chapter 16. Random walk in a dynamical random environment Appendix A. Analysis Appendix B. Probability Appendix C. Inequalities from statistical mechanics Appendix D. Nonnegative matrices
一般注記	Includes bibliographical references (pages 299-303) and indexes Access is restricted to licensed institutions Electronic reproduction Providence, Rhode Island American Mathematical Society 2015 Mode of access : World Wide Web Description based on print version record HTTP:URL=http://www.ams.org/gsm/162 Information=Contents HTTP:URL=https://doi.org/10.1090/gsm/162 Information=Contents

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