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<p>Interactions of the maxima and minima of the univariate functions appear in combinatorics as Dyck paths, and in topological data analysis as persistent homology. We study these descriptors for Brownian motions with drift, deriving the intensity measure and correlation functions for the persistence diagram point process <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\textbf{PH}_0\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="bold">PH</mi> <mn>0</mn> </msub> </math></EquationSource> </InlineEquation>, and quantifying the intrinsic asymmetries in the coupling of maxima and minima.</p>

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Brownian motions, persistent homology and chirality

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年11月25日

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  • Yuliy Baryshnikov

摘要

Interactions of the maxima and minima of the univariate functions appear in combinatorics as Dyck paths, and in topological data analysis as persistent homology. We study these descriptors for Brownian motions with drift, deriving the intensity measure and correlation functions for the persistence diagram point process \(\textbf{PH}_0\) PH 0 , and quantifying the intrinsic asymmetries in the coupling of maxima and minima.