Related papers: Three observations on spectra of zero-nonzero patt…
Random feature maps are ubiquitous in modern statistical machine learning, where they generalize random projections by means of powerful, yet often difficult to analyze nonlinear operators. In this paper, we leverage the "concentration"…
The aim of this paper is to establish some metrical coincidence and common fixed point theorems with an arbitrary relation under an implicit contractive condition which is general enough to cover a multitude of well known contraction…
The goal of the paper is to give a complete description of the images of noncommutative polynomials with zero constant term on upper triangular matrix algebras over an algebraically closed field. This is a variation of the old and famous…
It is shown that a random $(0,1)$ matrix whose rows are independent random vectors of exactly $n/2$ zero components is non-singular with probability $1-O(n^{-C})$ for any $C>0$. The proof uses a non-standard inverse-type Littlewood-Offord…
We give a combinatorial characterization of generic frameworks that are minimally rigid under the additional constraint of maintaining symmetry with respect to a finite order rotation or a reflection. To establish these results we develop a…
We consider the problem of enumerating permutations in the symmetric group on $n$ elements which avoid a given set of consecutive pattern $S$, and in particular computing asymptotics as $n$ tends to infinity. We develop a general method…
I shall present a proof of universality of the microscopic spectral correlations in Verbaarschot's random matrix models of QCD, to corroborate the beautiful agreement between the predictions from the gaussian model and the numerical data.…
A general overview of neutrino physics is given, starting with a historical account of the development of our understanding of neutrinos and how they helped to unravel the structure of the Standard Model. We discuss why it is so important…
We review some important results by Gross, Hacking, Keel, and Kontsevich on cluster algebra theory, namely, the column sign-coherence of $C$-matrices and the Laurent positivity, both of which were conjectured by Fomin and Zelevinsky. We…
By nonstandard analysis, a very short and elementary proof of the Spectral Theorem for unbounded self-adjoint operators is given.
Motivated by a recent work on a preconditioned MINRES for flipped linear systems in imaging, in this note we extend the scope of that research for including more precise boundary conditions such as reflective and anti-reflective ones. We…
We prove a generalization of the well-known theorems by Borg and Hochstadt for periodic self-adjoint Schr\"odinger operators without a spectral gap, respectively, one gap in their spectrum, in the matrix-valued context. Our extension of the…
We prove bounds for a class of unital homomorphisms arising in the study of spectral sets, by involving extremal functions and vectors. These are used to recover three celebrated results on spectral constants by Crouzeix--Palencia,…
We study some spectral properties of a matrix that is constructed as a combination of a Laplacian and an adjacency matrix of simple graphs. The matrix considered depends on a positive parameter, as such we consider the implications in…
In this paper spectral theorems for not necessarily continuous normal and self-adjoint random operators on a complex separable Hilbert space are proved.
Moments of secular and inverse secular coefficients, averaged over random matrices from classical groups, are related to the enumeration of non-negative matrices with prescribed row and column sums. Similar random matrix averages are…
This review provides a succinct overview of the basic aspects of neutrino physics. The topics covered include: neutrinos in the standard model and the three-neutrino mixing scheme; the current status of neutrino oscillation measurements and…
In this paper we study the Rotor Model of Martins and Nienhuis. After introducing spectral parameters, a combined use of integrability, polynomiality of the ground state wave function and a mapping into the fully-packed O(1)-model allows us…
The application of random matrix theory to scattering requires introduction of system-specific information. This paper shows that the average impedance matrix, which characterizes such system-specific properties, can be semiclassically…
We consider planar maps adjusted with a (regular critical) Boltzmann distribution and show that the expected number of pattern occurrences of a given map is asymptotically linear when the number n of edges goes to infinity. The main…