44 citations · 138 across the 32 of their papers we have counts for
6 papers · 1 filter
Probabilistic Schubert Calculus: asymptotics
Antonio Lerario, Léo Mathis
In the recent paper [arXiv:1612.06893] P. Bürgisser and A. Lerario introduced a geometric framework for a probabilistic study of real Schubert Problems. They denoted by t…
Betti Numbers of Random Hypersurface Arrangements
Saugata Basu, Antonio Lerario, Abhiram Natarajan
We study the expected behavior of the Betti numbers of arrangements of the zeros of random (distributed according to the Kostlan distribution) polynomials in $\mathbb{R}\mathrm{P}^…
Quantitative singularity theory for random polynomials
Paul Breiding, Hanieh Keneshlou, Antonio Lerario
Motivated by Hilbert's 16th problem we discuss the probabilities of topological features of a system of random homogeneous polynomials. The distribution for the polynomials is the…
-adic Integral Geometry
Avinash Kulkarni, Antonio Lerario
We prove a -adic version of the Integral Geometry Formula for averaging the intersection of two -adic projective algebraic sets. We apply this result to give bounds on the nu…
Random geometric complexes and graphs on Riemannian manifolds in the thermodynamic limit
Antonio Lerario, Raffaella Mulas
We investigate some topological properties of random geometric complexes and random geometric graphs on Riemannian manifolds in the thermodynamic limit. In particular, for random g…
Differential Topology of Gaussian Random Fields
Antonio Lerario, Michele Stecconi
Motivated by numerous questions in random geometry, given a smooth manifold , we approach a systematic study of the differential topology of Gaussian random fields (GRF) $X:M\to…