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標(biāo)題: Titlebook: Random Walks on Infinite Groups; Steven P. Lalley Textbook 2023 The Editor(s) (if applicable) and The Author(s), under exclusive license t [打印本頁]

作者: cessation    時(shí)間: 2025-3-21 16:29
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作者: 自制    時(shí)間: 2025-3-21 20:17
Subadditivity and Its Ramifications,Every random walk on a finitely generated group Γ whose step distribution has a finite first moment — that is, such that .|..|? 作者: GILD    時(shí)間: 2025-3-22 04:28
Entropy,In Chapter . we showed that the Liouville property is equivalent to triviality of the invariant .-algebra, and that this in turn is equivalent to weakly ergodicity of the underlying Markov chain. For random walks on finitely generated groups there is another equivalent condition.
作者: Adenocarcinoma    時(shí)間: 2025-3-22 07:03
Steven P. LalleyFirst textbook devoted solely to random walks on infinite, nonabelian groups.Integrated treatment of measure-theoretic probability and random walk theory.First textbook to treat Kleiner’s approach to
作者: CHURL    時(shí)間: 2025-3-22 08:58
978-3-031-25634-9The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl
作者: nurture    時(shí)間: 2025-3-22 12:53
Random Walks on Infinite Groups978-3-031-25632-5Series ISSN 0072-5285 Series E-ISSN 2197-5612
作者: 遭遇    時(shí)間: 2025-3-22 20:41

作者: 修飾    時(shí)間: 2025-3-22 21:40

作者: myopia    時(shí)間: 2025-3-23 04:46

作者: 叢林    時(shí)間: 2025-3-23 08:55

作者: 兇殘    時(shí)間: 2025-3-23 13:24
Isoperimetric Inequalities and Amenability,ughly like .., where .?≤?1 is the so-called . of the walk. When is it the case that this exponential rate . is strictly less than 1? Kesten [.] discovered that the answer depends on a fundamental structural feature of the ambient group: .
作者: 笨重    時(shí)間: 2025-3-23 15:13
Compact Group Actions and Boundaries,al objects. We have seen that the action of a finitely generated group on its Cayley graph by right multiplication is of fundamental importance in the study of random walks. In this chapter we will investigate group actions on . metric spaces, and show how these can unlock information about the long-time behavior of random walk trajectories.
作者: 正常    時(shí)間: 2025-3-23 21:22
Hyperbolic Groups,roup. In this chapter, we shall study a large class of groups, the ., first introduced by Gromov (Essays in Group Theory. Springer, New York, 1987), whose geometry forces certain regularities on random walk paths.
作者: 微不足道    時(shí)間: 2025-3-23 23:39
The Ergodic Theorem,to its initial location ..?=?1 is positive. Moreover, for any . the sequence . is a version of the random walk, as its increments .., .., ? are independent and identically distributed with common distribution ., and so the probability that it will ever return to the initial state 1 is also .?>?0.
作者: 形容詞    時(shí)間: 2025-3-24 05:48

作者: Ossification    時(shí)間: 2025-3-24 10:32
Isoperimetric Inequalities and Amenability,ughly like .., where .?≤?1 is the so-called . of the walk. When is it the case that this exponential rate . is strictly less than 1? Kesten [.] discovered that the answer depends on a fundamental structural feature of the ambient group: .
作者: Abjure    時(shí)間: 2025-3-24 12:45

作者: Myocyte    時(shí)間: 2025-3-24 18:04
Martingales,a finite region . is uniquely determined by its values on the boundary .. Consequently, for any finite region . the vector space of real harmonic functions in . is isomorphic to the space of real-valued functions on the boundary .. Is there an analogous characterization of the space of harmonic func
作者: paleolithic    時(shí)間: 2025-3-24 21:21

作者: congenial    時(shí)間: 2025-3-25 00:34
Hyperbolic Groups,roup. In this chapter, we shall study a large class of groups, the ., first introduced by Gromov (Essays in Group Theory. Springer, New York, 1987), whose geometry forces certain regularities on random walk paths.
作者: 希望    時(shí)間: 2025-3-25 06:54
Markov Chains and Harmonic Functions,natural setting for the theory is the world of countable-state .. Random walks on finitely generated groups are Markov chains; as we will see, so are a number of auxiliary processes constructed from random walks.
作者: semble    時(shí)間: 2025-3-25 08:33
Martingales,tions in . is isomorphic to the space of real-valued functions on the boundary .. Is there an analogous characterization of the space of harmonic functions on the entire state space? The answer, as we will show in Chapter ., is tied up with the limiting behavior of harmonic functions along Markov chain paths.
作者: canonical    時(shí)間: 2025-3-25 13:08

作者: CHECK    時(shí)間: 2025-3-25 17:48

作者: Banquet    時(shí)間: 2025-3-25 22:54
archers.Includes supplementary material: .The Encyclopedia of Mathematics Education is a comprehensive reference text, covering every topic in the field with entries ranging from short descriptions to much longer pieces where the topic warrants more elaboration. The entries provide access to theorie
作者: mortuary    時(shí)間: 2025-3-26 02:43
Steven Lalleyptions to much longer pieces where the topic warrants more elaboration. The entries provide access to theories and to research in the area and refer to the leading publications for further reading. The Encyclopedia is aimed at graduate students, researchers, curriculum developers, policy makers, and
作者: 人類    時(shí)間: 2025-3-26 04:59

作者: PACK    時(shí)間: 2025-3-26 08:33

作者: Eviction    時(shí)間: 2025-3-26 16:40

作者: 行為    時(shí)間: 2025-3-26 18:00

作者: 使?jié)M足    時(shí)間: 2025-3-26 23:30
Steven Lalleyptions to much longer pieces where the topic warrants more elaboration. The entries provide access to theories and to research in the area and refer to the leading publications for further reading. The Encyclopedia is aimed at graduate students, researchers, curriculum developers, policy makers, and
作者: CRAFT    時(shí)間: 2025-3-27 02:09
Steven Lalley from around the globe.Provides a comprehensive reference te.The Encyclopedia of Mathematics Education is a comprehensive reference text, covering every topic in the field with entries ranging from short descriptions to much longer pieces where the topic warrants more elaboration. The entries provid
作者: 小官    時(shí)間: 2025-3-27 05:53

作者: Pert敏捷    時(shí)間: 2025-3-27 09:27
Steven Lalley from around the globe.Provides a comprehensive reference te.The Encyclopedia of Mathematics Education is a comprehensive reference text, covering every topic in the field with entries ranging from short descriptions to much longer pieces where the topic warrants more elaboration. The entries provid
作者: 命令變成大炮    時(shí)間: 2025-3-27 16:45

作者: 親愛    時(shí)間: 2025-3-27 18:05

作者: 哥哥噴涌而出    時(shí)間: 2025-3-28 01:59

作者: ovation    時(shí)間: 2025-3-28 02:34

作者: 嚴(yán)厲批評(píng)    時(shí)間: 2025-3-28 08:50
Steven Lalleyptions to much longer pieces where the topic warrants more elaboration. The entries provide access to theories and to research in the area and refer to the leading publications for further reading. Links will also be made to particular texts in Springer journals and e-books through SpringerReference
作者: 現(xiàn)暈光    時(shí)間: 2025-3-28 10:33

作者: compassion    時(shí)間: 2025-3-28 18:11

作者: FLAG    時(shí)間: 2025-3-28 21:49

作者: prolate    時(shí)間: 2025-3-29 02:19
Steven Lalleyhematics, new frameworks for analysis of mathematics classrooms, and using simulations in mathematics teacher education. ?.Existing entries will be revised and new entries written. Members of978-3-030-15789-0
作者: conscience    時(shí)間: 2025-3-29 03:21
Steven Lalleyhematics, new frameworks for analysis of mathematics classrooms, and using simulations in mathematics teacher education. ?.Existing entries will be revised and new entries written. Members of978-3-030-15789-0




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