2 citations · 3 across the 3 of their papers we have counts for
13 papers
Large deviations for the volume of -nearest neighbor balls
Christian Hirsch, Taegyu Kang, Takashi Owada
This paper develops the large deviations theory for the point process associated with the Euclidean volume of -nearest neighbor balls centered around the points of a homogeneous…
Large deviations for subcomplex counts and Betti numbers in multi-parameter simplicial complexes
Gennady Samorodnitsky, Takashi Owada
We consider the multi-parameter random simplicial complex as a higher dimensional extension of the classical Erdös-Rényi graph. We investigate appearance of "unusual" topological s…
Convergence of persistence diagram in the sparse regime
Takashi Owada
The objective of this paper is to examine the asymptotic behavior of persistence diagrams associated with Čech filtration. A persistence diagram is a graphical descriptor of a topo…
Functional strong law of large numbers for Betti numbers in the tail
Takashi Owada, Zifu Wei
The objective of this paper is to investigate the layered structure of topological complexity in the tail of a probability distribution. We establish the functional strong law of l…
Functional strong laws of large numbers for Euler characteristic processes of extreme sample clouds
Andrew M. Thomas, Takashi Owada
To recover the topology of a manifold in the presence of heavy tailed or exponentially decaying noise, one must understand the behavior of geometric complexes whose points lie in t…
Limit theorems for topological invariants of the dynamic multi-parameter simplicial complex
Takashi Owada, Gennady Samorodnitsky, Gugan Thoppe
Topological study of existing random simplicial complexes is non-trivial and has led to several seminal works. However, the applicability of such studies is limited since the rando…