无约束 Sierpinski 地毯上的 Dirichlet 形式

IF 1.5 1区数学 Q2 STATISTICS & PROBABILITY Probability Theory and Related Fields Pub Date : 2024-04-12 DOI:10.1007/s00440-024-01280-6

Shiping Cao, Hua Qiu

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引用次数: 0

摘要

我们在无约束 Sierpinski 地毯上构建了对称自相似 Dirichlet 形式，通过允许小单元离开 1/k 网格而自然扩展了平面 Sierpinski 地毯。两个单元格的交点可以是一条长度为无理数的线段，而非对角线的假设在这种循环设置中被取消了。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Dirichlet forms on unconstrained Sierpinski carpets

We construct symmetric self-similar Dirichlet forms on unconstrained Sierpinski carpets, which are natural extension of planar Sierpinski carpets by allowing the small cells to live off the 1/k grids. The intersection of two cells can be a line segment of irrational length, and the non-diagonal assumption is dropped in this recurrent setting.

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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.