44 citations · 47 across the 3 of their papers we have counts for
6 papers
The distribution of the length of the longest path in random acyclic orientations of a complete bipartite graph
Jessica Khera, Erik Lundberg
Randomly sampling an acyclic orientation on the complete bipartite graph with parts of size and , we investigate the length of the longest path. We provide a proba…
On the average number of zeros of random harmonic polynomials with i.i.d. coefficients: precise asymptotics
Erik Lundberg, Andrew Thomack
Addressing a problem posed by W. Li and A. Wei (2009), we investigate the average number of (complex) zeros of a random harmonic polynomial sampled from th…
Multiplane gravitational lenses with an abundance of images
Charles R. Keeton, Erik Lundberg, Sean Perry
We consider gravitational lensing of a background source by a finite system of point-masses. The problem of determining the maximum possible number of lensed images has been comple…
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…
Experiments on the zeros of harmonic polynomials using certified counting
Jonathan D. Hauenstein, Antonio Lerario, Erik Lundberg +1
Motivated by Wilmshurst's conjecture, we investigate the zeros of harmonic polynomials. We utilize a certified counting approach which is a combination of two methods from numerica…
On the number of connected components of random algebraic hypersurfaces
Yan Fyodorov, Antonio Lerario, Erik Lundberg
We study the expectation of the number of components of a random algebraic hypersurface defined by the zero set in projective space of a random homogen…