Asymptotic behavior of Toeplitz determinants with a delta function singularity

Asymptotic Behavior of Infinity Harmonic Functions Near an Isolated Singularity

In this paper, we prove that if n ≥ 2 and x0 is an isolated singularity of a non-negative infinity harmonic function u, then either x0 is a removable singularity of u or u(x) = u(x0) + c|x − x0| + o(|x − x0|) near x0 for some fixed constant c = 0. In particular, if x0 is nonremovable, then u has a local maximum or a local minimum at x0. We also prove a Bernstein-type theorem, which asserts that...

Asymptotic Behavior of Multivariate Reward Processes with Nonlinear Reward Functions

The Asymptotic Spectra of Banded Toeplitz and Quasi-Toeplitz Matrices

Toeplitz matrices occur in many mathematical as well as scientific and engineering investigations. This paper considers the spectra of banded Toeplitz and quasi-Toeplitz matrices with emphasis on non-normal matrices of arbitrarily large order and relatively small bandwidth. These are the type of matrices that appear in the investigation of stability and convergence of difference approximations ...

On lacunary Toeplitz determinants

By using Riemann–Hilbert problem based techniques, we obtain the asymptotic expansion of lacunary Toeplitz determinants detN [ cla−mb [ f ] ] generated by holomorhpic symbols, where la = a (resp. mb = b) except for a finite subset of indices a = h1, . . . , hn (resp. b = t1, . . . , tr). In addition to the usual Szegö asymptotics, our answer involves a determinant of size n + r.

Block - Toeplitz Determinants

We evaluate the Geiss-Leclerc-Schröer φ-map for shape modules over the preprojective algebra Λ of type c A1 in terms of matrix minors arising from the block-Toeplitz representation of the loop group SL2(L). Conjecturally these minors are among the cluster variables for coordinate rings of unipotent cells within SL2(L). In so doing we compute the Euler characteristic of any generalized flag vari...