Abstract. This paper is about analytic properties of single transfer matrices originating from general block-tridiagonal or banded matrices. Such matrices occur in various applications in physics and numerical analysis. The eigenvalues of the transfer matrix describe localization of eigenstates and are linked to the spectrum of the block tridiagonal matrix by a determinantal identity. If the bl...

We give a formula that expresses the Hilbert series of one-sided ladder determinantal rings, up to a trivial factor, in form of a determinant. This allows the convenient computation of these Hilbert series. The formula follows from a determinantal formula for a generating function for families of nonintersecting lattice paths that stay inside a one-sided ladder-shaped region, in which the paths...

We derive an integration by parts formula for functionals of determinantal processes on compact sets, completing the arguments of [5]. This is used to show the existence of a configuration-valued diffusion process which is non-colliding and admits the distribution of the determinantal process as reversible law. In particular, this approach allows us to build a concrete example of the associated...

The Drazin inverse solutions of the matrix equations AX = B, XA = B and AXB = D are considered in this paper. We use both the determinantal representations of the Drazin inverse obtained earlier by the author and in the paper. We get analogs of the Cramer rule for the Drazin inverse solutions of these matrix equations and using their for determinantal representations of solutions of some differ...

I study tropical geometry, in particular tropical curves, moduli, and determinantal varieties. I have written five papers in tropical geometry: three on tropical curves and their moduli [Cha11a, Cha11b, CMV11], and two on tropical determinantal varieties [CC09, CJR09], joint with D. Cartwright, A. N. Jensen, and E. Rubei. After a brief introduction to tropical geometry, I will propose four main...

We introduce a short-range correlation density functional defined with respect to a multi-determinantal reference which is meant to be used in a multi-determinantal extension of the Kohn–Sham scheme of density functional theory based on a long-range/short-range decomposition of the Coulomb electron–electron interaction. We construct the local density approximation for this functional and discus...

We derive the explicit form of the (g − 2)(g − 3)/2 linearly independent relations among the products of pairs in a basis of holomorphic abelian differentials in the case of canonical curves of genus g ≥ 4. It turns out that Petri’s relations remarkably match in determinantal conditions. We explicitly express the volume form on the moduli space M̂g of canonical curves induced by the Siegel metri...

Introduced by Okounkov and Reshetikhin in 2003, the Schur Process has been shown to be a determinantal point process, so that each of its correlation functions are determinants of minors of one correlation kernel matrix. In previous papers, this was derived using determinantal expressions of the skew-Schur functions; in this paper, we obtain this result in a different way, using the fact that t...

The goal of this paper is to determine Gröbner bases of powers of determinantal ideals and to show that the Rees algebras of (products of) determinantal ideals are normal and CohenMacaulay if the characteristic of the base field is non-exceptional. Our main combinatorial result is a generalization of Schensted’s Theorem on the Knuth–Robinson–Schensted correspondence. Mathematics Subject Classif...