历史上的格子树 历史上的格子树
Manuel Cabezas1, Alexander Fribergh2, Mark Holmes3
1Pontificia Universidad Católica de Chile, Santiago, Chile.
概括
我们表明,关键格子树的重新缩放的历史过程汇聚到历史的布朗运动. 这一发现对于理解树上的随机走路及其与超级布罗恩运动的融合至关重要.
科学领域:
- 可能性理论概率理论.
- 随机过程 随机过程
- 数学物理学的数学物理.
背景情况:
- 格子树是统计力学和概率学的基本结构.
- 了解这些树上的随机过程的行为对于各种应用至关重要.
- 之前的研究已经探索了树上的随机步行和分支过程,但对历史过程的极限定理不那么发达.
研究的目的:
- 为了建立一个功能极限定理用于与关键的扩散格子树相关的重新缩放的历史过程.
- 为了证明这些过程与历史布朗运动的融合.
- 为分析随机树的谱系结构提供基础.
主要方法:
- 使用来自测量值过程理论的技术.
- 在各种维度的关键分布式格子树上应用重新缩放参数.
- 利用功能极限定理来建立收性质.
主要成果:
- 证明了关键分布式格子树的重新缩放的历史过程与历史的布朗运动趋同.
- 建立了这些测量值过程的功能极限定理.
- 结果编码了底层随机树的家谱结构.
结论:
- 对历史布朗运动的收为研究树木上的随机结构提供了一个强大的工具.
- 这些发现对理解格子树上随机走路的行为有直接影响.
- 该研究有助于更广泛地了解随机过程及其在数学物理中的应用.
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