4 papers
math.MG2026
The Zaporozhets-Tarasov Conjecture on Mean Distances
Eric Shen
For a convex body let be the expected distance between two independent uniform points of , and let be the corresponding expectation for nor…
math.FA2026
On circular Kippenhahn curves and the Gau-Wang-Wu conjecture about nilpotent partial isometries
Eric Shen
We study linear operators on a finite-dimensional space whose Kippenhahn curves consist of concentric circles centered at the origin. We say that such operators have Circularity pr…
math.FA2026
On Kippenhahn curves of low rank partial isometries
Nikita Popov, Eric Shen, Ilya M. Spitkovsky
Conditions are established for rank three partial isometries to have circular components contained in their Kippenhahn curves. In particular, such matrices with circular numerical…
math.CO2025
Tighter Bounds on the Expected Absorbing Time of Ungarian Markov Chains
Eric Shen
In , Defant and Li defined the Ungarian Markov chain associated to a finite lattice . This Markov chain has state space , and from any state tr…