7 papers
Rayleigh-Residual Flow I: Normal Matrices
Eric Shen
We study the squared Rayleigh-residual functional on complex projective space and its negative gradient flow. For an arbitrary complex matrix, every positive-residual critical poin…
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…
Learning Gaussian Graphical Models from a Glauber Trajectory Without Mixing
Eric Shen, Tony Wu, Mahbod Majid +1
We study the task of learning the structure of a -sparse Gaussian graphical model on variables from a single trajectory of Glauber dynamics. Beyond algorithmic consideration…
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…
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…
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…
On Effective Sato-Tate Distributions for Surfaces Arising from Products of Elliptic Curves
Quanlin Chen, Eric Shen
We prove, with an unconditional effective error bound, the Sato-Tate distributions for two families of surfaces arising from products of elliptic curves, namely a one-parameter fam…