随机轨道之间的最小距离

IF 1.5 1区数学 Q2 STATISTICS & PROBABILITY

Probability Theory and Related Fields Pub Date : 2024-05-11 DOI:10.1007/s00440-024-01283-3

Sébastien Gouëzel, Jérôme Rousseau, Manuel Stadlbauer

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引用次数: 0

摘要

我们研究的是在具有足够好的混合特性的随机动力系统中，长度为 n 的两个轨道段之间的最小距离。这个问题已经在非随机动力学系统和随机动力学系统的平均值中得到了解决（即所谓的退火版问题）：众所周知，这个问题的渐近行为是由一个与不变度量相关联的类似维度的量给出的，这个量被称为相关维度（或雷尼熵）。我们研究了类似的淬火问题，结果表明渐近行为更复杂：出现了两个相关维度，导致相关渐近指数的非平滑行为。

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Minimal distance between random orbits

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Minimal distance between random orbits

We study the minimal distance between two orbit segments of length n, in a random dynamical system with sufficiently good mixing properties. This problem has already been solved in non-random dynamical system, and on average in random dynamical systems (the so-called annealed version of the problem): it is known that the asymptotic behavior for this question is given by a dimension-like quantity associated to the invariant measure, called correlation dimension (or Rényi entropy). We study the analogous quenched question, and show that the asymptotic behavior is more involved: two correlation dimensions show up, giving rise to a non-smooth behavior of the associated asymptotic exponent.

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来源期刊

Probability Theory and Related Fields 数学-统计学与概率论

CiteScore

3.70

自引率

5.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Probability Theory and Related Fields publishes research papers in modern probability theory and its various fields of application. Thus, subjects of interest include: mathematical statistical physics, mathematical statistics, mathematical biology, theoretical computer science, and applications of probability theory to other areas of mathematics such as combinatorics, analysis, ergodic theory and geometry. Survey papers on emerging areas of importance may be considered for publication. The main languages of publication are English, French and German.