Theory of random matrices with strong level confinement: orthogonal polynomial approach

Strongly non-Gaussian ensembles of large random matrices possessing unitary symmetry and logarithmic level repulsion are studied both in presence and absence of hard edge in their energy spectra. Employing a theory of polynomials orthogonal with respect to exponential weights we calculate with asymptotic accuracy the two-point kernel over all distance scale, and show that in the limit of large dimensions of random matrices the properly rescaled local eigenvalue correlations are independent of level confinement while global smoothed connected correlations depend on confinement potential only through the endpoints of spectrum. We also obtain exact expressions for density of levels, one- and two-point Green's functions, and prove that new universal local relationship exists for suitably normalized and rescaled connected two-point Green's function. Connection between structure of Szeg\"o function entering strong polynomial asymptotics and mean-field equation is traced.Comment: 12 pages (latex), to appear in Physical Review

Multipoint Schur algorithm and orthogonal rational functions: convergence properties, I

Classical Schur analysis is intimately connected to the theory of orthogonal polynomials on the circle [Simon, 2005]. We investigate here the connection between multipoint Schur analysis and orthogonal rational functions. Specifically, we study the convergence of the Wall rational functions via the development of a rational analogue to the Szeg\H o theory, in the case where the interpolation points may accumulate on the unit circle. This leads us to generalize results from [Khrushchev,2001], [Bultheel et al., 1999], and yields asymptotics of a novel type.Comment: a preliminary version, 39 pages; some changes in the Introduction, Section 5 (Szeg\H o type asymptotics) is extende

A pedestrian's view on interacting particle systems, KPZ universality, and random matrices

These notes are based on lectures delivered by the authors at a Langeoog seminar of SFB/TR12 "Symmetries and universality in mesoscopic systems" to a mixed audience of mathematicians and theoretical physicists. After a brief outline of the basic physical concepts of equilibrium and nonequilibrium states, the one-dimensional simple exclusion process is introduced as a paradigmatic nonequilibrium interacting particle system. The stationary measure on the ring is derived and the idea of the hydrodynamic limit is sketched. We then introduce the phenomenological Kardar-Parisi-Zhang (KPZ) equation and explain the associated universality conjecture for surface fluctuations in growth models. This is followed by a detailed exposition of a seminal paper of Johansson that relates the current fluctuations of the totally asymmetric simple exclusion process (TASEP) to the Tracy-Widom distribution of random matrix theory. The implications of this result are discussed within the framework of the KPZ conjecture.Comment: 52 pages, 4 figures; to appear in J. Phys. A: Math. Theo

Design, Performance and Calibration of the CMS Forward Calorimeter Wedges

We report on the test beam results and calibration methods using charged particles of the CMS Forward Calorimeter (HF). The HF calorimeter covers a large pseudorapidity region (3\l |\eta| \le 5), and is essential for large number of physics channels with missing transverse energy. It is also expected to play a prominent role in the measurement of forward tagging jets in weak boson fusion channels. The HF calorimeter is based on steel absorber with embedded fused-silica-core optical fibers where Cherenkov radiation forms the basis of signal generation. Thus, the detector is essentially sensitive only to the electromagnetic shower core and is highly non-compensating (e/h \approx 5). This feature is also manifest in narrow and relatively short showers compared to similar calorimeters based on ionization. The choice of fused-silica optical fibers as active material is dictated by its exceptional radiation hardness. The electromagnetic energy resolution is dominated by photoelectron statistics and can be expressed in the customary form as a/\sqrt{E} + b. The stochastic term a is 198% and the constant term b is 9%. The hadronic energy resolution is largely determined by the fluctuations in the neutral pion production in showers, and when it is expressed as in the electromagnetic case, a = 280% and b = 11%

Design, Performance, and Calibration of CMS Hadron-Barrel Calorimeter Wedges

Extensive measurements have been made with pions, electrons and muons on four production wedges of the Compact Muon Solenoid (CMS) hadron barrel (HB) calorimeter in the H2 beam line at CERN with particle momenta varying from 20 to 300 GeV/c. Data were taken both with and without a prototype electromagnetic lead tungstate crystal calorimeter (EB) in front of the hadron calorimeter. The time structure of the events was measured with the full chain of preproduction front-end electronics running at 34 MHz. Moving-wire radioactive source data were also collected for all scintillator layers in the HB. These measurements set the absolute calibration of the HB prior to first pp collisions to approximately 4%

Design, Performance, and Calibration of the CMS Hadron-Outer Calorimeter

The CMS hadron calorimeter is a sampling calorimeter with brass absorber and plastic scintillator tiles with wavelength shifting fibres for carrying the light to the readout device. The barrel hadron calorimeter is complemented with an outer calorimeter to ensure high energy shower containment in the calorimeter. Fabrication, testing and calibration of the outer hadron calorimeter are carried out keeping in mind its importance in the energy measurement of jets in view of linearity and resolution. It will provide a net improvement in missing \et measurements at LHC energies. The outer hadron calorimeter will also be used for the muon trigger in coincidence with other muon chambers in CMS

Wild Plant Genetic Resources in North America: An Overview

North America, including Canada, Mexico, and the United States, is rich in plant species used by humans in both ancient and modern times. A select number of these have become globally important domesticated crops, including maize, beans, cotton, and sunflower. Many other native and also naturalized species have potential for use, either directly or as genetic resources for breeding agricultural crops. However, despite increasing recognition of their potential value, deficiencies in information, conservation, and access to the diversity in these plants hinder their further use. This chapter provides an overview of the agriculturally relevant wild plant resources of North America, with focus on wild relatives of globally important major crops, as well as the wild cousins of regionally and locally important domesticates. The chapter concludes by providing an overview of strategies for conserving wild plant genetic resources, including the international regulatory frameworks affecting policies to various degrees in Canada, Mexico, and the United States