快速不均的移民流程的过渡时间
Hwai-Ray Tung1, Sean D Lawley1
1Department of Mathematics, University of Utah, Salt Lake City, Utah 84112, USA.
Chaos (Woodbury, N.Y.)
|December 18, 2025
概括
这项研究研究了随着时间的推移而到达的搜索者如何影响生物物理系统中的目标寻找时间. 它证明了移民过程,即使是随机到达,也允许准确的极端价值分布.
科学领域:
- 生物物理学的生物物理.
- 随机过程 随机过程
- 可能性理论概率理论.
背景情况:
- 许多生物物理系统依赖于众多随机搜索者的快速目标检测.
- 经典模型通常假设所有搜索者最初都存在,从而使标准的极值理论成为可能.
- 这种假设限制了对连续搜索者到达的系统的适用性.
研究的目的:
- 调查时间依赖的寻求者移民对 kth 过境时间的影响.
- 为搜索者动态到达的系统开发数学模型.
- 在不均质移民下分析极端价值分布.
主要方法:
- 在不均的移民流程中探索 kth 路程时间.
- 严格证明分布和移民率时刻的趋同.
- 结合论证将时间不均的移民与初始存在模式联系起来.
- 分析作为一种移民形式的Yule (纯生) 过程.
主要成果:
- 证实了 kth 过渡时间的收,无论是时间不均的还是Yule 移民.
- 时间不均的移民通过合与经典模型有关.
- 耶鲁移民被证明相当于随机时间转移的时间不均过程.
- 圣诞节移民的极端价值分布与经典的弗雷切特,冈贝尔和韦布尔家族有所不同.
结论:
- 不均的移民过程为某些生物物理搜索问题提供了更现实的框架.
- 该研究为非独立的,非相同分布的随机变量推导了精确的极端值分布.
- 结果为具有动态搜索者群体的系统提供了洞察力,扩展了经典的极端价值理论.
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