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Kalikow问题研究 被引量:1

Study of Kalikow Problem
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摘要 通过概率论中的一般方法与数论中技巧相结合,本文证明了Kalikow问题中的随机环境中随机游动是非常返的。 Random walk'in a random environment, a process where a randomly chosen transition probability is assigned to each point, has been exhausivly studied in the one dimensional nearest neighbor case but is much more difficult in any more general case. I-n particular, in the two dimensional case little thing is known exept Theorem 1 0f (1). It is far from optimal and Kailikow proposed Problem 4 of (1), i.e., one of the below two environment is chosen to each point of Z2 in an i.i.d. manner woth the same probability.Is this R.W.I.R.E. recurent? The conclusion of Problem 4 of (1) seems obvious, but none of the previous, techniques seems to handl it exhausively. Conbining the technique of Number Theory with the general methods of Probability theory, we get that R.W.I.R.E. satisfying (*) is transient.
出处 《应用概率统计》 CSCD 北大核心 1996年第2期159-164,共6页 Chinese Journal of Applied Probability and Statistics
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