44 citations · 138 across the 32 of their papers we have counts for
5 papers · 1 filter
Low degree approximation of random polynomials
Daouda Niang Diatta, Antonio Lerario
We prove that with "high probability" a random Kostlan polynomial in many variables and of degree can be approximated by a polynomial of "low degree" without changing the…
Topologies of random geometric complexes on Riemannian manifolds in the thermodynamic limit
Antonio Auffinger, Antonio Lerario, Erik Lundberg
We investigate the topologies of random geometric complexes built over random points sampled on Riemannian manifolds in the so-called "thermodynamic" regime. We prove the existence…
On the geometry of the set of symmetric matrices with repeated eigenvalues
Paul Breiding, Khazhgali Kozhasov, Antonio Lerario
We investigate some geometric properties of the real algebraic variety of symmetric matrices with repeated eigenvalues. We explicitly compute the volume of its intersection wit…
Zeroes of polynomials on definable hypersurfaces: pathologies exist, but they are rare
Saugata Basu, Antonio Lerario, Abhiram Natarajan
Given a sequence of smooth and compact hypersurfaces in , we prove that (up to extracting subsequences) there exists a regular definab…
Volume of small balls and sub-Riemannian curvature in 3D contact manifolds
Davide Barilari, Ivan Beschastnyi, Antonio Lerario
We compute the asymptotic expansion of the volume of small sub-Riemannian balls in a contact 3-dimensional manifold, and we express the first meaningful geometric coefficients in t…