Strong asymptotics for Cauchy biorthogonal polynomials with application to the Cauchy two--matrix model

We apply the nonlinear steepest descent method to a class of 3x3 Riemann-Hilbert problems introduced in connection with the Cauchy two-matrix random model. The general case of two equilibrium measures supported on an arbitrary number of intervals is considered. In this case, we solve the Riemann-Hilbert problem for the outer parametrix in terms of sections of a spinorial line bundle on a three-sheeted Riemann surface of arbitrary genus and establish strong asymptotic results for the Cauchy biorthogonal polynomials.Comment: 31 pages, 12 figures. V2; typos corrected, added reference

Critical behavior in Angelesco ensembles

We consider Angelesco ensembles with respect to two modified Jacobi weights on touching intervals [a,0] and [0,1], for a < 0. As a \to -1 the particles around 0 experience a phase transition. This transition is studied in a double scaling limit, where we let the number of particles of the ensemble tend to infinity while the parameter a tends to -1 at a rate of order n^{-1/2}. The correlation kernel converges, in this regime, to a new kind of universal kernel, the Angelesco kernel K^{Ang}. The result follows from the Deift/Zhou steepest descent analysis, applied to the Riemann-Hilbert problem for multiple orthogonal polynomials.Comment: 32 pages, 9 figure

Large n limit of Gaussian random matrices with external source, Part III: Double scaling limit

We consider the double scaling limit in the random matrix ensemble with an external source \frac{1}{Z_n} e^{-n \Tr({1/2}M^2 -AM)} dM defined on $n\times n$ Hermitian matrices, where $A$ is a diagonal matrix with two eigenvalues $\pm a$ of equal multiplicities. The value $a=1$ is critical since the eigenvalues of $M$ accumulate as $n \to \infty$ on two intervals for $a > 1$ and on one interval for $0 < a < 1$. These two cases were treated in Parts I and II, where we showed that the local eigenvalue correlations have the universal limiting behavior known from unitary random matrix ensembles. For the critical case $a=1$ new limiting behavior occurs which is described in terms of Pearcey integrals, as shown by Br\'ezin and Hikami, and Tracy and Widom. We establish this result by applying the Deift/Zhou steepest descent method to a $3 \times 3$-matrix valued Riemann-Hilbert problem which involves the construction of a local parametrix out of Pearcey integrals. We resolve the main technical issue of matching the local Pearcey parametrix with a global outside parametrix by modifying an underlying Riemann surface.Comment: 36 pages, 9 figure

Continuous variable private quantum channel

In this paper we introduce the concept of quantum private channel within the continuous variables framework (CVPQC) and investigate its properties. In terms of CVPQC we naturally define a "maximally" mixed state in phase space together with its explicit construction and show that for increasing number of encryption operations (which sets the length of a shared key between Alice and Bob) the encrypted state is arbitrarily close to the maximally mixed state in the sense of the Hilbert-Schmidt distance. We bring the exact solution for the distance dependence and give also a rough estimate of the necessary number of bits of the shared secret key (i.e. how much classical resources are needed for an approximate encryption of a generally unknown continuous-variable state). The definition of the CVPQC is analyzed from the Holevo bound point of view which determines an upper bound of information about an incoming state an eavesdropper is able to get from his optimal measurement.Comment: upper bound on information Eve can get was revised and substantially lowered (chapter IV), part of chapter III rewritten, several typos correcte

Historic buildings and the creation of experiencescapes: looking to the past for future success

Purpose: The purpose of this paper is to identify the role that the creative re-use of historic buildings can play in the future development of the experiences economy. The aesthetic attributes and the imbued historic connotation associated with the building help create unique and extraordinary “experiencescapes” within the contemporary tourism and hospitality industries. Design/methodology/approach: This paper provides a conceptual insight into the creative re-use of historic buildings in the tourism and hospitality sectors, the work draws on two examples of re-use in the UK. Findings: This work demonstrates how the creative re-use of historic buildings can help create experiences that are differentiated from the mainstream hospitality experiences. It also identifies that it adds an addition unquantifiable element that enables the shift to take place from servicescape to experiencescape. Originality/value: There has been an ongoing debate as to the significance of heritage in hospitality and tourism. However, this paper provides an insight into how the practical re-use of buildings can help companies both benefit from and contribute to the experiences economy

Quantum Distribution of Gaussian Keys with Squeezed States

A continuous key distribution scheme is proposed that relies on a pair of canonically conjugate quantum variables. It allows two remote parties to share a secret Gaussian key by encoding it into one of the two quadrature components of a single-mode electromagnetic field. The resulting quantum cryptographic information vs disturbance tradeoff is investigated for an individual attack based on the optimal continuous cloning machine. It is shown that the information gained by the eavesdropper then simply equals the information lost by the receiver.Comment: 5 pages, RevTe