91 citations · 603 across the 31 of their papers we have counts for
25 papers · 1 filter
Critical radii and suprema of random waves over Riemannian manifolds
Renjie Feng, Dong Yao, Robert J. Adler
We study random waves on smooth, compact, Riemannian manifolds under the spherical ensemble. Our first main result shows that there is a positive universal limit for the critical r…
Central Limit Theorems for Local Functionals of Dynamic Point Processes
Efe Onaran, Omer Bobrowski, Robert J. Adler
We establish finite-dimensional central limit theorems for local, additive, interaction functions of temporally evolving point processes. The dynamics are those of a spatial Poisso…
Functional Central Limit Theorems for Local Statistics of Spatial Birth-Death Processes in the Thermodynamic Regime
Efe Onaran, Omer Bobrowski, Robert J. Adler
We present normal approximation results at the process level for local functionals defined on dynamic Poisson processes in . The dynamics we study here are those of a…
On the Spectrum of Dense Random Geometric Graphs
Kartick Adhikari, Robert J. Adler, Omer Bobrowski +1
In this paper we study the spectrum of the random geometric graph , in a regime where the graph is dense and highly connected. In the \erdren random graph it is we…
Critical radius and supremum of random spherical harmonics (II)
Renjie Feng, Xingcheng Xu, Robert J. Adler
We continue the study, begun in \cite{FA}, of the critical radius of embeddings, via deterministic spherical harmonics, of fixed dimensional spheres into higher dimensional ones, a…
Critical radius and supremum of random spherical harmonics
Renjie Feng, Robert J. Adler
We first consider {\it deterministic} immersions of the -dimensional sphere into high dimensional Euclidean spaces, where the immersion is via spherical harmonics of level .…
The Intrinsic Geometry of Some Random Manifolds
Sunder Ram Krishnan, Jonathan E. Taylor, Robert J. Adler
We study the a.s. convergence of a sequence of random embeddings of a fixed manifold into Euclidean spaces of increasing dimensions. We show that the limit is deterministic. As a c…
A central limit theorem for the Euler integral of a Gaussian random field
Gregory Naitzat, Robert J. Adler
Euler integrals of deterministic functions have recently been shown to have a wide variety of possible applications, including in signal processing, data aggregation and network se…
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…
On the evolution of topology in dynamic clique complexes
Gugan Thoppe, D. Yogeshwaran, Robert Adler
We consider a time varying analogue of the Erd{\H o}s-R{\' e}nyi graph and study the topological variations of its associated clique complex. The dynamics of the graph are stationa…
Convergence of the Reach for a Sequence of Gaussian-Embedded Manifolds
Robert J. Adler, Sunder Ram Krishnan, Jonathan E. Taylor +1
Motivated by questions of manifold learning, we study a sequence of random manifolds, generated by embedding a fixed, compact manifold into Euclidean spheres of increasing dime…
Climbing down Gaussian peaks
Robert Adler, Gennady Samorodnitsky
How likely is the high level of a continuous Gaussian random field on an Euclidean space to have a "hole" of a certain dimension and depth? Questions of this type are difficult, bu…
Random geometric complexes in the thermodynamic regime
D. Yogeshwaran, Eliran Subag, Robert J. Adler
We consider the topology of simplicial complexes with vertices the points of a random point process and faces determined by distance relationships between the vertices. In particul…
Crackle: The Persistent Homology of Noise
Robert J. Adler, Omer Bobrowski, Shmuel Weinberger
We study the homology of simplicial complexes built via deterministic rules from a random set of vertices. In particular, we show that, depending on the randomness that generates t…
On the topology of random complexes built over stationary point processes
D. Yogeshwaran, Robert J. Adler
There has been considerable recent interest, primarily motivated by problems in applied algebraic topology, in the homology of random simplicial complexes. We consider the scenario…
On the existence of paths between points in high level excursion sets of Gaussian random fields
Robert J. Adler, Elina Moldavskaya, Gennady Samorodnitsky
The structure of Gaussian random fields over high levels is a well researched and well understood area, particularly if the field is smooth. However, the question as to whether or…
Rotation and scale space random fields and the Gaussian kinematic formula
Robert J. Adler, Eliran Subag, Jonathan E. Taylor
We provide a new approach, along with extensions, to results in two important papers of Worsley, Siegmund and coworkers closely tied to the statistical analysis of fMRI (functional…
Distance Functions, Critical Points, and the Topology of Random Čech Complexes
Omer Bobrowski, Robert J. Adler
For a finite set of points in , the function measures Euclidean distance to the set . We study the number of critical points of when is a P…
Efficient Monte Carlo for high excursions of Gaussian random fields
Robert J. Adler, Jose H. Blanchet, Jingchen Liu
Our focus is on the design and analysis of efficient Monte Carlo methods for computing tail probabilities for the suprema of Gaussian random fields, along with conditional expectat…
Persistent Homology for Random Fields and Complexes
Robert J. Adler, Omer Bobrowski, Matthew S. Borman +2
We discuss and review recent developments in the area of applied algebraic topology, such as persistent homology and barcodes. In particular, we discuss how these are related to un…
High level excursion set geometry for non-Gaussian infinitely divisible random fields
Robert J. Adler, Gennady Samorodnitsky, Jonathan E. Taylor
We consider smooth, infinitely divisible random fields , , with regularly varying Levy measure, and are interested in the geometric characte…
Global geometry under isotropic Brownian flows
Sreekar Vadlamani, Robert J. Adler
We consider global geometric properties of a codimension one manifold embedded in Euclidean space, as it evolves under an isotropic and volume preserving Brownian flow of diffeomor…
Some New Random Field Tools for Spatial Analysis
Robert J Adler
This is a brief review, in relatively non-technical terms, of recent advances in the theory of random field geometry. These advances have provided a collection of explicit new form…
Excursion sets of stable random fields
Robert J. Adler, Gennady Samorodnitsky, Jonathan E. Taylor
Studying the geometry generated by Gaussian and Gaussian- related random fields via their excursion sets is now a well developed and well understood subject. The purely non-Gaussia…