Related papers: Operator limit of the circular beta ensemble
We prove a general inequality on $\beta$-mixing coefficients of point processes depending uniquely on their $n$-th order intensity functions. We apply this inequality in the case of determinantal point processes and show that the rate of…
In many iterative optimization methods, fixed-point theory enables the analysis of the convergence rate via the contraction factor associated with the linear approximation of the fixed-point operator. While this factor characterizes the…
It is well known that there are entire functions whose orbit approximates any other entire function under the action of a sequence of translation operators . This result also holds for an uncountable family of sequences of translation…
The boundary operator is a linear operator that acts on a collection of high-dimensional binary points (simplices) and maps them to their boundaries. This boundary map is one of the key components in numerous applications, including…
We give a simple proof of a central limit theorem for linear statistics of the Circular beta-ensembles which is valid at almost arbitrary mesoscopic scale and for functions of class C^3. As a consequence, using a coupling introduced by…
We consider the notion of real center of mass and total center of mass of a bounded linear operator relative to another bounded linear operator and explore their relation with cosine and total cosine of a bounded linear operator acting on a…
The hard edge and bulk scaling limits of $\beta$-ensembles are described by the stochastic Bessel and sine operators, which are respectively a random Sturm-Liouville operator and a random Dirac operator. By representing both operators as…
The $\beta$-functions describe how couplings run under the renormalization group flow in field theories. In general, all couplings that respect the symmetry and locality are generated under the renormalization group flow, and the exact…
This note is a survey and collection of results, as well as presenting some original research. For Bessel sequences and frames, the analysis, synthesis and frame operators as well as the Gram matrix are well-known, bounded operators. We…
In this paper, we study the operator equation $AB=\lambda BA$ for a bounded operator $A,B$ on a complex Hilbert space. We focus on algebraic relations between different operators that include normal, $M$-hyponormal, quasi $*$-paranormal and…
In this paper we describe an iterative operator-splitting method for unbounded operators. We derive error bounds for iterative splitting methods in the presence of unbounded operators and semigroup operators. Here mixed applications of…
We study topological boundedness of order-to-topology bounded and order-to-topology continuous operators from ordered vector spaces to topological vector spaces. The uniform boundedness principle for such operators is investigated.
Frames have been investigated frequently over the last few decades due to their valuable properties, which are desirable for various applications as well as interesting for theory. Some applications additionally require distributed…
We construct Baxter operators for the homogeneous closed $\mathrm{XXX}$ spin chain with the quantum space carrying infinite or finite dimensional $s\ell_2$ representations. All algebraic relations of Baxter operators and transfer matrices…
This article presents a new proof of a theorem concerning bounds of the spectrum of the product of unitary operators and a generalization for differentiable curves of this theorem. The proofs involve metric geometric arguments in the group…
In this paper, we prove a polynomial Central Limit Theorem for several integrable models, and for the $\beta$-ensembles at high-temperature with polynomial potential. Furthermore, we connect the mean values, the variances and the…
Some results on fixed points related to the contractive compositions of bounded operators in complete metric spaces are discussed through the manuscript. The class of composite operators under study can include, in particular, sequences of…
We describe in terms of automata theory the automatic actions with post-critically finite limit space. We prove that these actions are precisely the actions by bounded automata and that any self-similar action by bounded automata is…
We provide several perturbation theorems regarding closable operators on a real or complex Hilbert space. In particular we extend some classical results due to Hess--Kato, Kato--Rellich and W\"ust. Our approach involves ranges of matrix…
We study persistent Betti numbers and persistence diagrams obtained from time series and random fields. It is well known that the persistent Betti function is an efficient descriptor of the topology of a point cloud. So far, convergence…