TY - JOUR
T1 - A limit theorem for persistence diagrams of random filtered complexes built over marked point processes
AU - Shirai, Tomoyuki
AU - Suzaki, Kiyotaka
N1 - Funding Information:
This work was supported by JST CREST Grant Number JPMJCR15D3, Japan. The first named author (T.S.) was supported by JSPS KAKENHI Grant Numbers JP18H01124, JP20K20884, and JSPS Grant-in-Aid for Transformative Research Areas (A) JP22H05105. T.S. was also supported in part by JSPS KAKENHI Grant Numbers, JP20H00119 and JP21H04432.
Publisher Copyright:
© 2023 The Author(s).
PY - 2023/1
Y1 - 2023/1
N2 - Random filtered complexes built over marked point processes on Euclidean spaces are considered. Examples of these filtered complexes include a filtration of Čech complexes of a family of sets with various sizes, growths, and shapes. The law of large numbers for persistence diagrams is established as the size of the convex window observing a marked point process tends to infinity.
AB - Random filtered complexes built over marked point processes on Euclidean spaces are considered. Examples of these filtered complexes include a filtration of Čech complexes of a family of sets with various sizes, growths, and shapes. The law of large numbers for persistence diagrams is established as the size of the convex window observing a marked point process tends to infinity.
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U2 - 10.15559/22-VMSTA214
DO - 10.15559/22-VMSTA214
M3 - Article
AN - SCOPUS:85144532174
SN - 2351-6046
VL - 10
SP - 1
EP - 18
JO - Modern Stochastics: Theory and Applications
JF - Modern Stochastics: Theory and Applications
IS - 1
ER -