3 citations · 7 across the 9 of their papers we have counts for
12 papers
A Hyperfinite Framework for Score-Based Generative Modeling
Sunder Ram Krishnan
Score-based diffusion models are typically formulated using continuous-time stochastic differential equations and measure-theoretic stochastic calculus. In this paper, we develop a…
Cartan meets Cramér-Rao
Sunder Ram Krishnan
A Cartan-geometric, jet bundle formulation of curvature-aware variance bounds in parametric statistical estimation is developed. Building on our earlier extrinsic Hilbert space app…
Rao-Blackwellized Coverage Estimation in Poisson Networks: A High-Fidelity Hybrid Framework
Sunder Ram Krishnan, Junaid Farooq, Kumar Vijay Mishra +3
While stochastic geometry provides a powerful framework for the analysis of cellular networks, standard Monte Carlo simulations often suffer from slow convergence due to the stocha…
Refining Cramér-Rao Bound With Multivariate Parameters: An Extrinsic Geometry Perspective
Sunder Ram Krishnan
We derive a vector generalization of the curvature-corrected Cramér--Rao bound (CRB) in the nonasymptotic regime using a Hilbert space square-root embedding. Building on previous s…
Improving Cramér-Rao Bound And Its Variants: An Extrinsic Geometry Perspective
Sunder Ram Krishnan
This work presents a geometric refinement of the classical Cramér--Rao bound (CRB) in the non-asymptotic regime by incorporating curvature-aware corrections based on the second fun…
Restricted Quasiconvexity Isometry Property for Symmetric -Stable Random Matrices
Sunder Ram Krishnan
We formulate a generalization of the Restricted Isometry Property (RIP) referred to as the Restricted Quasiconvexity Isometry Property (RQIP) for alpha stable random projections wi…
Coherent Source Enumeration with Compact ULAs
Dibakar Sil, Sunder Ram Krishnan, Kumar Vijay Mishra
Source enumeration typically relies on subspace-based techniques that require accurate separation of signal and noise subspaces. However, prior works do not address coherent source…
Betti Numbers of Gaussian Excursions in the Sparse Regime
Gugan Thoppe, Sunder Ram Krishnan
Random field excursions is an increasingly vital topic within data analysis in medicine, cosmology, materials science, etc. This work is the first detailed study of their Betti num…
Crossing Numbers of Random Two-Bridge Knots
Moshe Cohen, Chaim Even-Zohar, Sunder Ram Krishnan
In a previous work, the first and third authors studied a random knot model for all two-bridge knots using billiard table diagrams. Here we present a closed formula for the distrib…
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…
Random knots using Chebyshev billiard table diagrams
Moshe Cohen, Sunder Ram Krishnan
We use the Chebyshev knot diagram model of Koseleff and Pecker in order to introduce a random knot diagram model by assigning the crossings to be positive or negative uniformly at…
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…