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Extremal lifetimes of persistent cycles

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Extremal lifetimes of persistent cycles. / Chenavier, Nicolas; Hirsch, Christian.
In: Extremes, Vol. 25, No. 2, 06.2022, p. 299-330.

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaper › Journal article › Research › peer-review

Vancouver

Chenavier N, Hirsch C. Extremal lifetimes of persistent cycles. Extremes. 2022 Jun;25(2):299-330. doi: 10.1007/s10687-021-00430-6

Author

Chenavier, Nicolas ; Hirsch, Christian. / Extremal lifetimes of persistent cycles. In: Extremes. 2022 ; Vol. 25, No. 2. pp. 299-330.

Bibtex

@article{a6ae7b7efb9347a9ade9ba5feb19470f,

title = "Extremal lifetimes of persistent cycles",

abstract = "Persistent homology captures the appearances and disappearances of topological features such as loops and cavities when growing disks centered at a Poisson point process. We study extreme values for the lifetimes of features dying in bounded components and with birth resp. death time bounded away from the threshold for continuum percolation and the coexistence region. First, we describe the scaling of the minimal lifetimes for general feature dimensions, and of the maximal lifetimes for cavities in the Cech filtration. Then, we proceed to a more refined analysis and establish Poisson approximation for large lifetimes of cavities and for small lifetimes of loops. Finally, we also study the scaling of minimal lifetimes in the Vietoris-Rips setting and point to a surprising difference to the Cech filtration.",

keywords = "Topological data analysis, Persistent Betti numbers, Poisson approximation, TOPOLOGY, LIMIT, 82C22, 60K35",

author = "Nicolas Chenavier and Christian Hirsch",

year = "2022",

month = jun,

doi = "10.1007/s10687-021-00430-6",

language = "English",

volume = "25",

pages = "299--330",

journal = "Extremes",

issn = "1386-1999",

publisher = "Springer",

number = "2",

}

RIS

TY - JOUR

T1 - Extremal lifetimes of persistent cycles

AU - Chenavier, Nicolas

AU - Hirsch, Christian

PY - 2022/6

Y1 - 2022/6

N2 - Persistent homology captures the appearances and disappearances of topological features such as loops and cavities when growing disks centered at a Poisson point process. We study extreme values for the lifetimes of features dying in bounded components and with birth resp. death time bounded away from the threshold for continuum percolation and the coexistence region. First, we describe the scaling of the minimal lifetimes for general feature dimensions, and of the maximal lifetimes for cavities in the Cech filtration. Then, we proceed to a more refined analysis and establish Poisson approximation for large lifetimes of cavities and for small lifetimes of loops. Finally, we also study the scaling of minimal lifetimes in the Vietoris-Rips setting and point to a surprising difference to the Cech filtration.

AB - Persistent homology captures the appearances and disappearances of topological features such as loops and cavities when growing disks centered at a Poisson point process. We study extreme values for the lifetimes of features dying in bounded components and with birth resp. death time bounded away from the threshold for continuum percolation and the coexistence region. First, we describe the scaling of the minimal lifetimes for general feature dimensions, and of the maximal lifetimes for cavities in the Cech filtration. Then, we proceed to a more refined analysis and establish Poisson approximation for large lifetimes of cavities and for small lifetimes of loops. Finally, we also study the scaling of minimal lifetimes in the Vietoris-Rips setting and point to a surprising difference to the Cech filtration.

KW - Topological data analysis

KW - Persistent Betti numbers

KW - Poisson approximation

KW - TOPOLOGY

KW - LIMIT

KW - 82C22

KW - 60K35

U2 - 10.1007/s10687-021-00430-6

DO - 10.1007/s10687-021-00430-6

M3 - Journal article

VL - 25

SP - 299

EP - 330

JO - Extremes

JF - Extremes

SN - 1386-1999

IS - 2

ER -