32 citations · 78 across the 24 of their papers we have counts for
24 papers
Layered Hill estimator for extreme data in clusters
Taegyu Kang, Takashi Owada
A new estimator is proposed for estimating the tail exponent of a heavy-tailed distribution. This estimator, referred to as the layered Hill estimator, is a generalization of the t…
Degree counts in random simplicial complexes of the preferential attachment type
Takashi Owada, Gennady Samorodnitsky
We extend the classical preferential attachment random graph model to random simplicial complexes. At each stage of the model, we choose one of the existing -simplices with prob…
Limit theorems for critical faces above the vanishing threshold
Zifu Wei, Takashi Owada, D. Yogeshwaran
We investigate convergence of point processes associated with critical faces for a Čech filtration built over a homogeneous Poisson point process in the -dimensional flat torus.…
Limit theorems for high-dimensional Betti numbers in the multiparameter random simplicial complexes
Takashi Owada, Gennady Samorodnitsky
We consider the multiparameter random simplicial complex on a vertex set , which is parameterized by multiple connectivity probabilities. Our key results concern t…
Large deviations for hyperbolic -nearest neighbor balls
Christian Hirsch, Moritz Otto, Takashi Owada +1
We prove a large deviation principle for the point process of large Poisson -nearest neighbor balls in hyperbolic space. More precisely, we consider a stationary Poisson point p…
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…
Large deviation principle for geometric and topological functionals and associated point processes
Christian Hirsch, Takashi Owada
We prove a large deviation principle for the point process associated to -element connected components in with respect to the connectivity radii . Th…
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…
Functional limit theorems for the Euler characteristic process in the critical regime
Andrew M. Thomas, Takashi Owada
This study presents functional limit theorems for the Euler characteristic of Vietoris-Rips complexes. The points are drawn from a non-homogeneous Poisson process on …
A functional non-central limit theorem for multiple-stable processes with long-range dependence
Shuyang Bai, Takashi Owada, Yizao Wang
A functional limit theorem is established for the partial-sum process of a class of stationary sequences which exhibit both heavy tails and long-range dependence. The stationary se…
Convergence of Persistence Diagrams for Topological Crackle
Takashi Owada, Omer Bobrowski
In this paper we study the persistent homology associated with topological crackle generated by distributions with an unbounded support. Persistent homology is a topological and al…
Limit theorems for process-level Betti numbers for sparse, critical, and Poisson regimes
Takashi Owada, Andrew Thomas
The objective of this study is to examine the asymptotic behavior of Betti numbers of Čech complexes treated as stochastic processes and formed from random points in the -dimens…
Sub-tree counts on hyperbolic random geometric graphs
Takashi Owada, D. Yogeshwaran
We study the hyperbolic random geometric graph introduced in Krioukov et al. For a sequence , we define these graphs to have the vertex set as Poisson points distri…
Limit Theorems for the Sum of Persistence Barcodes
Takashi Owada
Topological Data Analysis (TDA) refers to an approach that uses concepts from algebraic topology to study the "shapes" of datasets. The main focus of this paper is persistent homol…
Functional Central Limit Theorem for Subgraph Counting Processes
Takashi Owada
The objective of this study is to investigate the limiting behavior of a subgraph counting process. The subgraph counting process we consider counts the number of subgraphs having…
Functional central limit theorem for negatively dependent heavy-tailed stationary infinitely divisible processes generated by conservative flows
Paul Jung, Takashi Owada, Gennady Samorodnitsky
We prove a functional central limit theorem for partial sums of symmetric stationary long range dependent heavy tailed infinitely divisible processes with a certain type of negativ…
Limit Theorems for Point Processes under Geometric Constraints (and Topological Crackle)
Takashi Owada, Robert J. Adler
We study the asymptotic nature of geometric structures formed from a point cloud of observations of (generally heavy tailed) distributions in a Euclidean space of dimension greater…
Maxima of long memory stationary symmetric -stable processes, and self-similar processes with stationary max-increments
Takashi Owada, Gennady Samorodnitsky
We derive a functional limit theorem for the partial maxima process based on a long memory stationary -stable process. The length of memory in the stable process is parameterize…
Limit Theory for the Sample Autocovariance for Heavy Tailed Stationary Infinitely Divisible Processes Generated by Conservative Flows
Takashi Owada
This study aims to develop the limit theorems on the sample autocovariances and sample autocorrelations for certain stationary infinitely divisible processes. We consider the case…
Functional central limit theorem for heavy tailed stationary infinitely divisible processes generated by conservative flows
Takashi Owada, Gennady Samorodnitsky
We establish a new class of functional central limit theorems for partial sum of certain symmetric stationary infinitely divisible processes with regularly varying Lévy measures. T…