Block size in Geometric(p)-biased permutations

被引：1

作者：

Cristali, Irina ^{[1
]}

Ranjan, Vinit ^{[1
]}

Steinberg, Jake ^{[1
]}

Beckman, Erin ^{[1
]}

Durrett, Rick ^{[1
]}

Junge, Matthew ^{[1
]}

Nolen, James ^{[1
]}

机构：

[1] Duke Univ, Durham, NC 27706 USA

来源：

ELECTRONIC COMMUNICATIONS IN PROBABILITY | 2018年 / 23卷

关键词：

regenerative permutations; Bernoulli sieve; BERNOULLI SIEVE;

D O I：

10.1214/18-ECP182

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

Fix a probability distribution p = (p(1),p(2),...) on the positive integers. The first block in a p-biased permutation can be visualized in terms of raindrops that land at each positive integer j with probability p(j). It is the first point K so that all sites in [1, K] are wet and all sites in (K, infinity) are dry. For the geometric distribution p, = p(1 - p)(j-1) we show that p log K converges in probability to an explicit constant as p tends to 0. Additionally, we prove that if p has a stretch exponential distribution, then K is infinite with positive probability.

引用

页数：10

共 12 条

[1] Limit theorems for longest monotone subsequences in random Mallows permutations [J].