Related papers: On the limiting Horn inequalities
We give a minimal list of inequalities characterizing the possible eigenvalues of a set of Hermitian matrices with positive semidefinite sum of bounded rank. This answers a question of A. Barvinok.
We introduce and study a 2-parameter family of unitarily invariant probability measures on the space of infinite Hermitian matrices. We show that the decomposition of a measure from this family on ergodic components is described by a…
The multiplicative Horn problem is the following question: given three conjugacy classes $\mathcal{C}_1, \mathcal{C}_2, \mathcal{C}_3$ in a Lie group $G$, do there exist elements…
The main objective of this paper is to show that balls under invariant metrics on hyperbolic planar domains are finitely-connected. As applications, we give new and transparent proofs of classical results on conformal mappings of planar…
We study the representation theory of the infinite type A Hecke algebra over a non-archimedean field in the case where the parameter is a pseudo-uniformizer. Specifically, we consider a family of representations, called almost-symmetric,…
We obtain a general concept of triplet of Hilbert spaces with closed (unbounded) embeddings instead of continuous (bounded) ones. The construction starts with a positive selfadjoint operator $H$, that is called the Hamiltonian of the…
We prove that the point process of the eigenvalues of real or complex non-Hermitian matrices $X$ with independent, identically distributed entries is hyperuniform: the variance of the number of eigenvalues in a subdomain $\Omega$ of the…
Let $n\geq 2$ and $\Phi_{n,t,\pi}: M_n({\mathbb C}) \rightarrow M_n({\mathbb C})$ be a linear map defined by $\Phi_{n,t,\pi}(A)=(n-t)\sum_{i=1}^nE_{ii}AE_{ii}+t\sum_{i=1}^nE_{i,\pi(i)}AE_{i,\pi(i)}^\dag-A$, where $0\leq t\leq n$, $E_{ij}$s…
The infinite-dimensional unitary group U(infinity) is the inductive limit of growing compact unitary groups U(N). In this paper we solve a problem of harmonic analysis on U(infinity) stated in the previous paper math/0109193. The problem…
We establish a characterization of almost $P$-matrices via a sign non-reversal property. In this we are inspired by the analogous results for $N$-matrices. Next, the interval hull of two $m \times n$ matrices $A=(a_{ij})$ and $B =…
We prove that a nonsymmetric normal entry pattern of order $n$ ($n\ge 3$) has at most $n(n-3)/2+3$ distinct indeterminates and up to permutation similarity this number is attained by a unique pattern which is explicitly described.
A major challenge in the study of the structure of the three-dimensional homology cobordism group is to understand the interaction between hyperbolic geometry and homology cobordism. In this paper, for a hyperbolic homology sphere $Y$ we…
In his work on singularities, expanders and topology of maps, Gromov showed, using isoperimetric inequalities in graded algebras, that every real valued map on the $n$-torus admits a fibre whose homological size is bounded below by some…
We introduce a class of paired binary matrices called admixed arrays, which arise in analyses of large-scale genetic data and can be viewed as weighted edge colorings of complete bipartite graphs. This combinatorial structure gives rise to…
An orthoset is a set equipped with a symmetric, irreflexive binary relation. With any (anisotropic) Hermitian space $H$, we may associate the orthoset $(P(H),\perp)$, consisting of the set of one-dimensional subspaces of $H$ and the usual…
We consider changes in properties of a subgraph of an infinite graph resulting from the addition of open edges of Bernoulli percolation on the infinite graph to the subgraph. We give the triplet of an infinite graph, one of its subgraphs,…
Non-Hermitian Hamiltonians H possess the real (i.e., observable) spectra inside certain specific domains of parameters D. In general, the determination of their observability-horizon boundaries is difficult. We list the pseudo-Hermitian…
We review some convexity inequalities for Hermitian matrices an add one more to the list.
The spectrum of a non-Hermitian system generically forms a two-dimensional complex Riemannian manifold with distinct topology from the underlying parameter space. Spectral topology permits parametric loops to map the affiliated eigenvalue…
Covering a convex body by its homothets is a classical notion in discrete geometry that has resulted in a number of interesting and long-standing problems. Swanepoel introduced the covering parameter of a convex body as a means of…