91 citations · 603 across the 31 of their papers we have counts for
6 papers · 2 filters
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…