Searcharxiv⌕ Search

arXiv subjects

Dimbihery Rabenoro

Publications and source records attributed to Dimbihery Rabenoro.

5 recordsLinked to original sources
arXiv2025

Functional Erdős-Rényi laws for Lévy processes

In this paper we establish functional Erdős-Renyi laws for Lévy processes, i.e. limit theorems for sets of functions on [0,1] associated to their increments. First, we determine precise conditions under which, in a general framework, such a convergence is derived from a large deviations principle for probability measures induced by the sample paths of such a process. Then, by checking that these conditions are fulfilled, we obtain, under two usual assumptions on exponential moments, such limit theorems from well-known large deviations principles.

math.ST↗
arXiv2024

A geometric framework for asymptotic inference of principal subspaces in PCA

In this article, we develop an asymptotic method for constructing confidence regions for the set of all linear subspaces arising from PCA, from which we derive hypothesis tests on this set. Our method is based on the geometry of Riemannian manifolds with which some sets of linear subspaces are endowed.

math.ST↗
arXiv2024

Effective formulas for the geometry of normal homogeneous spaces. Application to flag manifolds

Consider a smooth manifold and an action on it of a compact connected Lie group with a bi-invariant metric. Then, any orbit is an embedded submanifold that is isometric to a normal homogeneous space for the group. In this paper, we establish new explicit and intrinsic formulas for the geometry of any such orbit. We derive our formula of the Levi-Civita connection from an existing generic formula for normal homogeneous spaces, i.e. which determines, a priori only theoretically, the connection. We say that our formulas are effective: they are directly usable, notably in numerical analysis, provided that the ambient manifold is convenient for computations. Then, we deduce new effective formulas for flag manifolds, since we prove that they are orbits under a suitable action of the special orthogonal group on a product of Grassmannians. This representation of them is quite useful, notably for studying flags of eigenspaces of symmetric matrices. Thus, we develop from it a geometric solution to the problem of perturbation of eigenvectors which is explicit and optimal in a certain sense, improving the classical analytic solution.

math.DG↗