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math.PR2016★ 10 cited
Limit theorems for persistence diagrams
Trinh Khanh Duy, Yasuaki Hiraoka, Tomoyuki Shirai
The persistent homology of a stationary point process on is studied in this paper. As a generalization of continuum percolation theory, we study higher dimensional topo…
math.PR2014★ 2 cited
Absolute continuity and singularity of Palm measures of the Ginibre point process
Hirofumi Osada, Tomoyuki Shirai
We prove a dichotomy between absolute continuity and singularity of the Ginibre point process and its reduced Palm measures $\{\mathsf{G}_{\mathbf{x}}, \mathbf{x} \in…