凶残
发表于 2025-3-23 13:24:12
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: .
笨重
发表于 2025-3-23 15:13:27
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.
正常
发表于 2025-3-23 21:22:41
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.
微不足道
发表于 2025-3-23 23:39:24
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.
形容词
发表于 2025-3-24 05:48:19
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Ossification
发表于 2025-3-24 10:32:24
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: .
Abjure
发表于 2025-3-24 12:45:22
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Myocyte
发表于 2025-3-24 18:04:40
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
paleolithic
发表于 2025-3-24 21:21:54
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congenial
发表于 2025-3-25 00:34:21
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.