Related papers: Partial trace relations beyond normal matrices
We explain how a slight variant in the use of our recursive algorithm leads to improve the known lower bounds for the absolute trace of a totally positive algebraic integer. We also link the absolute trace of a totally positive algebraic…
Variational convexity, together with ist strong counterpart, of extended-real-valued functions has been recently introduced by Rockafellar. In this paper we present second-order characterizations of these properties, i.e., conditions using…
This paper presents new probability inequalities for sums of independent, random, self-adjoint matrices. These results place simple and easily verifiable hypotheses on the summands, and they deliver strong conclusions about the…
We establish sharp-in-time kernel and dispersive estimates for the Schr\"odinger equation on non-compact Riemannian symmetric spaces of any rank. Due to the particular geometry at infinity and the Kunze-Stein phenomenon, these properties…
Stanley's inequalities for partially ordered sets establish important log-concavity relations for sequences of linear extensions counts. Their extremals however, i.e., the equality cases of these inequalities, were until now poorly…
We study the decomposability and the subdifferential of the tensor nuclear norm. Both concepts are well understood and widely applied in matrices but remain unclear for higher-order tensors. We show that the tensor nuclear norm admits a…
Patterned random matrices such as the reverse circulant, the symmetric circulant, the Toeplitz and the Hankel matrices and their almost sure limiting spectral distribution (LSD), have attracted much attention. Under the assumption that the…
We analyze the semiclassical Einstein equations for quantum scalar fields satisfying modified dispersion relations. We first discuss in detail the renormalization procedure based on adiabatic subtraction and dimensional regularization. We…
In this paper we present a tail inequality for the maximum of partial sums of a weakly dependent sequence of random variables that are not necessarily bounded. The class considered includes geometrically and subgeometrically strongly mixing…
We show that any finite dimensional von Neumann algebra admits an orthonormal unitary basis with respect to its standard trace. We also show that a finite dimensional von Neumann subalgebra of $M_n(\mathbb{C})$ admits an orthonormal unitary…
We consider the alternating sign matrices of the odd order that have some kind of central symmetry. Namely, we deal with matrices invariant under the half-turn, quarter-turn and flips in both diagonals. In all these cases, there are two…
In this paper, we prove a trace inequality $\text{Tr}[ f(A) A^s B^s ] \leq \text{Tr}[ f(A) (A^{1/2} B A^{1/2} )^s ]$ for any positive and monotone increasing function $f$, $s\in[0,1]$, and positive semi-definite matrices $A$ and $B$. On the…
Matrix pencils, or pairs of matrices, are used in a variety of applications. By the Kronecker decomposition Theorem, they admit a normal form. This normal form consists of four parts, one part based on the Jordan canonical form, one part…
We study an invariant, the secondary trace, attached to two commuting endomorphisms of a 2-dualizable object in a symmetric monoidal higher category. We establish a secondary trace formula which encodes the natural symmetries of this…
Asymmetric vector norms are generalizations of asymmetric norms, where the subadditivity inequality is understood in ordered vector space sense. This relation imposes strong conditions on the ordering itself. This note studies on these…
For any family of $N\times N$ random matrices $(\mathbf{A}_k)_{k\in K}$ which is invariant, in law, under unitary conjugation, we give general sufficient conditions for central limit theorems for random variables of the type…
In this paper, we introduce two new forms of the dual Hartwig-Spindelb{\"o}ck decomposition and employ them to derive explicit representations for several classes of dual generalized inverses. Building on these representations, we further…
For any additive functor from modules (or, more generally, from an abelian category with enough projectives or injectives), we construct long sequences tying up together the derived functors, the satellites, and the stabilizations of the…
Every commuting set of normal matrices with entries in an AW*-algebra can be simultaneously diagonalized. To establish this, a dimension theory for properly infinite projections in AW*-algebras is developed. As a consequence, passing to…
We study the distribution of the outliers in the spectrum of finite rank deformations of Wigner random matrice under the assumption that the off-diagonal matrix entries have uniformly bounded fifth moment and the diagonal entries have…