Linear Statistics of Point Processes via Orthogonal Polynomials

For arbitrary $\beta > 0$, we use the orthogonal polynomials techniques developed by R. Killip and I. Nenciu to study certain linear statistics associated with the circular and Jacobi $\beta$ ensembles. We identify the distribution of these statistics then prove a joint central limit theorem. In the circular case, similar statements have been proved using different methods by a number of authors. In the Jacobi case these results are new.Comment: Added references, corrected typos. To appear, J. Stat. Phy

On the Lebesgue measure of Li-Yorke pairs for interval maps

We investigate the prevalence of Li-Yorke pairs for $C^2$ and $C^3$ multimodal maps $f$ with non-flat critical points. We show that every measurable scrambled set has zero Lebesgue measure and that all strongly wandering sets have zero Lebesgue measure, as does the set of pairs of asymptotic (but not asymptotically periodic) points. If $f$ is topologically mixing and has no Cantor attractor, then typical (w.r.t. two-dimensional Lebesgue measure) pairs are Li-Yorke; if additionally $f$ admits an absolutely continuous invariant probability measure (acip), then typical pairs have a dense orbit for $f \times f$. These results make use of so-called nice neighborhoods of the critical set of general multimodal maps, and hence uniformly expanding Markov induced maps, the existence of either is proved in this paper as well. For the setting where $f$ has a Cantor attractor, we present a trichotomy explaining when the set of Li-Yorke pairs and distal pairs have positive two-dimensional Lebesgue measure.Comment: 41 pages, 3 figure

Tests of the Equivalence Principle with Neutral Kaons

We test the Principle of Equivalence for particles and antiparticles, using CPLEAR data on tagged K0 and K0bar decays into pi^+ pi^-. For the first time, we search for possible annual, monthly and diurnal modulations of the observables |eta_{+-}| and phi_{+-}, that could be correlated with variations in astrophysical potentials. Within the accuracy of CPLEAR, the measured values of |eta_{+-}| and phi_{+-} are found not to be correlated with changes of the gravitational potential. We analyze data assuming effective scalar, vector and tensor interactions, and we conclude that the Principle of Equivalence between particles and antiparticles holds to a level of 6.5, 4.3 and 1.8 x 10^{-9}, respectively, for scalar, vector and tensor potentials originating from the Sun with a range much greater than the distance Earth-Sun. We also study energy-dependent effects that might arise from vector or tensor interactions. Finally, we compile upper limits on the gravitational coupling difference between K0 and K0bar as a function of the scalar, vector and tensor interaction range.Comment: 15 pages latex 2e, five figures, one style file (cernart.csl) incorporate

Logarithmic and complex constant term identities

In recent work on the representation theory of vertex algebras related to the Virasoro minimal models M(2,p), Adamovic and Milas discovered logarithmic analogues of (special cases of) the famous Dyson and Morris constant term identities. In this paper we show how the identities of Adamovic and Milas arise naturally by differentiating as-yet-conjectural complex analogues of the constant term identities of Dyson and Morris. We also discuss the existence of complex and logarithmic constant term identities for arbitrary root systems, and in particular prove complex and logarithmic constant term identities for the root system G_2.Comment: 26 page

CHIME Discovery of a Binary Pulsar with a Massive Non-Degenerate Companion

Of the more than 3000 radio pulsars currently known, only ∼300 are in binary systems, and only five of these consist of young pulsars with massive nondegenerate companions. We present the discovery and initial timing, accomplished using the Canadian Hydrogen Intensity Mapping Experiment (CHIME) telescope, of the sixth such binary pulsar, PSR J2108+4516, a 0.577 s radio pulsar in a 269 day orbit of eccentricity 0.09 with a companion of minimum mass 11 M⊙. Notably, the pulsar undergoes periods of substantial eclipse, disappearing from the CHIME 400–800 MHz observing band for a large fraction of its orbit, and displays significant dispersion measure and scattering variations throughout its orbit, pointing to the possibility of a circumstellar disk or very dense stellar wind associated with the companion star. Subarcsecond resolution imaging with the Karl G. Jansky Very Large Array unambiguously demonstrates that the companion is a bright, V ≃ 11 OBe star, EM* UHA 138, located at a distance of 3.26(14) kpc. Archival optical observations of EM* UHA 138 approximately suggest a companion mass ranging from 17.5 M⊙ < Mc < 23 M⊙, in turn constraining the orbital inclination angle to 50fdg3 ≲ i ≲ 58fdg3. With further multiwavelength follow-up, PSR J2108+4516 promises to serve as another rare laboratory for the exploration of companion winds, circumstellar disks, and short-term evolution through extended-body orbital dynamics