文章基本信息

标题：Non-universality for longest increasing subsequence of a random walk
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作者：Robin Pemantle ; Yuval Peres
期刊名称：Latin American Journal of Probability and Mathematical Statistics
电子版ISSN：1980-0436
出版年度：2017
卷号：XIV
页码：327-336
出版社：Instituto Nacional De Matemática Pura E Aplicada
摘要：The longest increasing subsequence of a random walk with mean zeroand finite variance is known to be of length n1/2+o(1). We show that this is notuniversal for symmetric random walks. In particular, the symmetric Ultra-fat tailedrandom walk has a longest increasing subsequence that is asymptotically at leastn0.690 and at most n0.815. An exponent strictly greater than 1/2 is also shown forthe symmetric stable-α distribution when α is sufficiently small.
关键词：Ultra-fat tailed distribution; stable law; LIS; NBU.