149 research outputs found
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
Introduction to Random Matrices
These notes provide an introduction to the theory of random matrices. The
central quantity studied is where is the integral
operator with kernel 1/\pi} {\sin\pi(x-y)\over x-y} \chi_I(y). Here
and is the characteristic function
of the set . In the Gaussian Unitary Ensemble (GUE) the probability that no
eigenvalues lie in is equal to . Also is a tau-function
and we present a new simplified derivation of the system of nonlinear
completely integrable equations (the 's are the independent variables)
that were first derived by Jimbo, Miwa, M{\^o}ri, and Sato in 1980. In the case
of a single interval these equations are reducible to a Painlev{\'e} V
equation. For large we give an asymptotic formula for , which is
the probability in the GUE that exactly eigenvalues lie in an interval of
length .Comment: 44 page
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
Measurement of the Neutron Radius of 208Pb Through Parity-Violation in Electron Scattering
We report the first measurement of the parity-violating asymmetry A_PV in the
elastic scattering of polarized electrons from 208Pb. A_PV is sensitive to the
radius of the neutron distribution (Rn). The result A_PV = 0.656 \pm 0.060
(stat) \pm 0.014 (syst) ppm corresponds to a difference between the radii of
the neutron and proton distributions Rn - Rp = 0.33 +0.16 -0.18 fm and provides
the first electroweak observation of the neutron skin which is expected in a
heavy, neutron-rich nucleus.Comment: 6 pages, 1 figur
The impact of Stieltjes' work on continued fractions and orthogonal polynomials
Stieltjes' work on continued fractions and the orthogonal polynomials related
to continued fraction expansions is summarized and an attempt is made to
describe the influence of Stieltjes' ideas and work in research done after his
death, with an emphasis on the theory of orthogonal polynomials
Misunderstandings Concerning Genetics Among Patients Confronting Genetic Disease
Critical questions arise about misunderstandings of genetics. We interviewed for 2 h each, 64 individuals who had or were at risk for Huntington's disease (HD), breast cancer or Alpha‐1 antitrypsin deficiency. These individuals revealed various misunderstandings that can affect coping, and testing, treatment and reproductive decisions. A therapeutic misconception about testing appeared: that testing would be helpful in and of itself. Many believed they could control genetic disorders (even HD), yet these beliefs were often incorrect, and could impede coping, testing, and treatment. Misunderstandings about statistics and genetics often fueled each other, and reflected denial, and desires for hope and control. Emotional needs can thus outweigh understandings of genetics and statistics, and providers’ input. Individuals often maintained non‐scientific beliefs, though embarrassed by these. These data have implications for care, and public and professional education. Misunderstandings’ persistence, despite realization of their inaccuracy, suggests that providers need to address not just cognitive facts, but underlying emotional issues
Timing and Tempo of Early and Successive Adaptive Radiations in Macaronesia
The flora of Macaronesia, which encompasses five Atlantic archipelagos (Azores, Canaries, Madeira, Cape Verde, and Salvage), is exceptionally rich and diverse
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%
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