Maximum gaps in one-dimensional hard-core models

IF 0.5 4区 数学 Q4 STATISTICS & PROBABILITY
Dingding Dong, Nitya Mani
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引用次数: 0

Abstract

We study the distribution of the maximum gap size in one-dimensional hard-core models. First, we sequentially pack rods of length 2 into an interval of length L at random, subject to the hard-core constraint that rods do not overlap. We find that in a saturated packing, with high probability there is no gap of size 2−o(L−1) between adjacent rods, but there are gaps of size at least 2−Lε−1 for all ε>0. We subsequently study a dependent thinning-based variant of the hard-core process, the one-dimensional “ghost” hard-core model. In this model, we sequentially pack rods of length 2 into an interval of length L at random, such that placed rods neither overlap with previously placed rods nor previously considered candidate rods. We find that in the infinite time limit, with high probability the maximum gap between adjacent rods is smaller than logL but at least (logL)1−ε for all ε>0.
一维硬核模型的最大间隙
我们研究了一维硬核模型中最大间隙尺寸的分布。首先,我们按顺序将长度为2的棒随机装入长度为L的区间中,并遵守棒不重叠的核心约束。我们发现在饱和填料中,相邻棒材之间很可能不存在大小为2−0 (L−1)的间隙,但对于所有ε>0的棒材都存在大小至少为2−Lε−1的间隙。我们随后研究了一种基于依赖变薄的硬核过程,即一维“幽灵”硬核模型。在该模型中,我们将长度为2的棒随机排列到长度为L的区间中,这样放置的棒既不会与先前放置的棒重叠,也不会与先前考虑的候选棒重叠。我们发现,在无限时限内,相邻杆之间的最大间距大概率小于logL,但对于所有ε>0的点,最大间距至少为(logL)1−ε。
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来源期刊
Electronic Communications in Probability
Electronic Communications in Probability 工程技术-统计学与概率论
CiteScore
1.00
自引率
0.00%
发文量
38
审稿时长
6-12 weeks
期刊介绍: The Electronic Communications in Probability (ECP) publishes short research articles in probability theory. Its sister journal, the Electronic Journal of Probability (EJP), publishes full-length articles in probability theory. Short papers, those less than 12 pages, should be submitted to ECP first. EJP and ECP share the same editorial board, but with different Editors in Chief.
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