44 citations · 138 across the 32 of their papers we have counts for
4 papers · 1 filter
Gap probabilities and applications to geometry and random topology
Antonio Lerario, Erik Lundberg
We give an exact formula for the value of the derivative at zero of the gap probability in finite n x n Gaussian ensembles. As n goes to infinity our computation provides an asympt…
Remarks on Wilmshurst's theorem
Seung-Yeop Lee, Antonio Lerario, Erik Lundberg
We demonstrate counterexamples to Wilmshurst's conjecture on the valence of harmonic polynomials in the plane, and we conjecture a bound that is linear in the analytic degree for e…
Statistics on Hilbert's Sixteenth Problem
Antonio Lerario, Erik Lundberg
We study the statistics of the number of connected components and the volume of a random real algebraic hypersurface in RP^n defined by a Real Bombieri-Weyl distributed homogeneous…
Geometry of Maslov cycles
Davide Barilari, Antonio Lerario
We introduce the notion of induced Maslov cycle, which describes and unifies geometrical and topological invariants of many apparently unrelated problems, from Real Algebraic Geome…