Zobrazeno 1 - 10
of 163
pro vyhledávání: '"Lundberg, Erik P."'
Autor:
Khera, Jessica, Lundberg, Erik
Randomly sampling an acyclic orientation on the complete bipartite graph $K_{n,k}$ with parts of size $n$ and $k$, we investigate the length of the longest path. We provide a probability generating function for the distribution of the longest path le
Externí odkaz:
http://arxiv.org/abs/2408.12716
Autor:
Lundberg, Erik, Thomack, Andrew
Addressing a problem posed by W. Li and A. Wei (2009), we investigate the average number of (complex) zeros of a random harmonic polynomial $p(z) + \overline{q(z)}$ sampled from the Kac ensemble, i.e., where the coefficients are independent identical
Externí odkaz:
http://arxiv.org/abs/2308.10333
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 completely resolved in the single-plane setting (where the point masses all
Externí odkaz:
http://arxiv.org/abs/2302.11735
Investigating a problem posed by W. Hengartner (2000), we study the maximal valence (number of preimages of a prescribed point in the complex plane) of logharmonic polynomials, i.e., complex functions that take the form $f(z) = p(z) \overline{q(z)}$
Externí odkaz:
http://arxiv.org/abs/2302.04339
A classically studied geometric property associated to a complex polynomial $p$ is the inradius (the radius of the largest inscribed disk) of its (filled) lemniscate $\Lambda := \{z \in \mathbb{C}:|p(z)| < 1\}$. In this paper, we study the lemniscate
Externí odkaz:
http://arxiv.org/abs/2301.13424
Autor:
Lundberg, Erik
Publikováno v:
Proc. Amer. Math. Soc. 151 (2023), 2963-2973
We prove the existence of complex polynomials $p(z)$ of degree $n$ and $q(z)$ of degree $m
Externí odkaz:
http://arxiv.org/abs/2201.00788
We consider the average number of limit cycles that bifurcate from a randomly perturbed linear center where the perturbation consists of random (bivariate) polynomials with independent coefficients. This problem reduces, by way of classical perturbat
Externí odkaz:
http://arxiv.org/abs/2112.05672
We consider the critical points (equilibria) of a planar potential generated by $n$ Newtonian point masses augmented with a quadratic term (such as arises from a centrifugal effect). Particular cases of this problem have been considered previously in
Externí odkaz:
http://arxiv.org/abs/2106.11416
Autor:
Lundberg, Erik
We study the number and distribution of the limit cycles of a planar vector field whose component functions are random polynomials. We prove a lower bound on the average number of limit cycles when the random polynomials are sampled from the Kostlan-
Externí odkaz:
http://arxiv.org/abs/2007.00724
Autor:
Khavinson, Dmitry, Lundberg, Erik
We prove the existence of a roof function for arclength null quadrature domains having finitely many boundary components. This bridges a gap toward classification of arclength null quadrature domains by removing an a priori assumption from previous c
Externí odkaz:
http://arxiv.org/abs/2005.09822