How to find an extra head: Optimal random shifts of Bernoulli and Poisson random fields
成果类型：
Article
署名作者：
Holroyd, AE; Liggett, TM
署名单位：
University of California System; University of California Los Angeles
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
发表日期：
2001
页码：
1405-1425
关键词：
摘要：
We consider the following problem: given an i.i.d. family of Bernoulli random variables indexed by Z(d), find a random occupied site X is an element of Z(d) such that relative to X, the other random variables are still i.i.d. Bernoulli. Results of Thorisson imply that such an X exists for all d. Liggett proved that for d = 1, there exists an X with tails P(\X\ greater than or equal to t) of order ct(-1/2), but none with finite 1/2th moment. We prove that for general d there exists a solution with tails of order ct(-d/2), while for d = 2 there is none with finite first moment. We also prove analogous results for a continuum version of the same problem. Finally we prove a result which strongly suggests that the tail behavior mentioned above is the best possible for all d.