44 citations · 138 across the 32 of their papers we have counts for
4 papers · 1 filter
Probabilistic Schubert Calculus
Peter Bürgisser, Antonio Lerario
We initiate the study of average intersection theory in real Grassmannians. We define the expected degree of the real Grassmannian as the average nu…
Random fields and the enumerative geometry of lines on real and complex hypersurfaces
Saugata Basu, Antonio Lerario, Erik Lundberg +1
We derive a formula expressing the average number of real lines on a random hypersurface of degree in in terms of the expected modulus of the…
Homotopically Invisible Singular Curves
Andrei A. Agrachev, Francesco Boarotto, Antonio Lerario
Given a smooth manifold and a totally nonholonomic distribution of rank , we study the effect of singular curves on the topology of the space of horizontal pat…
On the geometry of random lemniscates
Antonio Lerario, Erik Lundberg
We investigate the geometry of a random rational lemniscate , the level set on the Riemann sphere of the modulus of a random rational function . We assign a pr…