Related papers: Comparing with octopi
In this paper we develop a general theoretical tool for the establishment of the boundedness of notoriously difficult operators (such as potentials) on certain specific types of rearrangement-invariant function spaces from analogous…
Quantum walks on graphs are ubiquitous in quantum computing finding a myriad of applications. Likewise, random walks on graphs are a fundamental building block for a large number of algorithms with diverse applications. While the…
We completely characterize Birkhoff-James orthogonality with respect to numerical radius norm in the space of bounded linear operators on a complex Hilbert space. As applications of the results obtained, we estimate lower bounds of…
This article is concerned with numerical methods to approximate effective coefficients in stochastic homogenization of discrete linear elliptic equations, and their numerical analysis --- which has been made possible by recent contributions…
In this paper we study some determinant inequalities and matrix inequalities which have a geometrical flavour. We first examine some inequalities which place work of Macbeath [13] in a more general setting and also relate to recent work of…
The study of several naturally arising "nearest neighbours" random walks benefits from the study of the associated orthogonal polynomials and their orthogonality measure. I consider extensions of this approach to a larger class of random…
Quantum walks have by now been realized in a large variety of different physical settings. In some of these, particularly with trapped ions, the walk is implemented in phase space, where the corresponding position states are not orthogonal.…
This article implements a simple convex approach and block techniques to obtain several new refined versions of numerical radius inequalities for Hilbert space operators. This includes comparisons among the norms of the operators, their…
This is the second part of a series of four articles on weighted norm inequalities, off-diagonal estimates and elliptic operators. We consider a substitute to the notion of pointwise bounds for kernels of operators which usually is a…
We show that in the space of nuclear operators from $\ell^q(\Lambda)$ to $\ell^p(J)$ the two natural ways of measuring weak non-compactness coincide. We also provide explicit formulas for these measures. As a consequence the same is proved…
Recently, several groups have investigated quantum analogues of random walk algorithms, both on a line and on a circle. It has been found that the quantum versions have markedly different features to the classical versions. Namely, the…
In this paper, we establish the quantitative mean ergodic theorems for two subclasses of power bounded operators on a fixed noncommutative $L_p$-space with $1<p<\infty$, which mainly concerns power bounded invertible operators and Lamperti…
Using known entropic and information inequalities new inequalities for some classical polynomials are obtained. Examples of Jacobi and Legendre polynomials are considered.
Some new inequalities for the norm and the numerical radius of composite operators generated by a pair of operators are given.
We investigate Sobolev inequalities for several rough operators. We prove that several operators satisfy a pointwise bound by the Riesz potential applied to the gradient. From this inequality, we derive several new Sobolev-type inequalities…
Although quantum walks exhibit peculiar properties that distinguish them from random walks, classical behavior can be recovered in the asymptotic limit by destroying the coherence of the pure state associated to the quantum system. Here I…
We consider the operator associated to a random walk on finite volume surfaces with hyperbolic cusps. We study the spectral gap (upper and lower bound) associated to this operator and deduce some rate of convergence of the iterated kernel…
Given the extensive application of classical random walks to classical algorithms in a variety of fields, their quantum analogue in quantum walks is expected to provide a fruitful source of quantum algorithms. So far, however, such…
We establish some weighted $L^2$ inequalities for Fourier extension operators in the setting of orthonormal systems. In the process we develop a direct approach to such inequalities based on generalised Wigner distributions, complementing…
Quantum versions of random walks on the line and the cycle show a quadratic improvement over classical random walks in their spreading rates and mixing times respectively. Non-unitary quantum walks can provide a useful optimisation of these…