Bethe anzats derivation of the Tracy-Widom distribution for one-dimensional directed polymers

The distribution function of the free energy fluctuations in one-dimensional directed polymers with $\delta$-correlated random potential is studied by mapping the replicated problem to a many body quantum boson system with attractive interactions. Performing the summation over the entire spectrum of excited states the problem is reduced to the Fredholm determinant with the Airy kernel which is known to yield the Tracy-Widom distributionComment: 5 page

Heat Capacity of ^3He in Aerogel

The heat capacity of pure ^3He in low density aerogel is measured at 22.5 bar. The superfluid response is simultaneously monitored with a torsional oscillator. A slightly rounded heat capacity peak, 65 mu K in width, is observed at the ^3He-aerogel superfluid transition, T_{ca}. Subtracting the bulk ^3He contribution, the heat capacity shows a Fermi-liquid form above T_{ca}. The heat capacity attributed to superfluid within the aerogel can be fit with a rounded BCS form, and accounts for 0.30 of the non-bulk fluid in the aerogel, indicating a substantial reduction in the superfluid order parameter consistent with earlier superfluid density measurements.Comment: 4 pages, 5 figure

From interacting particle systems to random matrices

In this contribution we consider stochastic growth models in the Kardar-Parisi-Zhang universality class in 1+1 dimension. We discuss the large time distribution and processes and their dependence on the class on initial condition. This means that the scaling exponents do not uniquely determine the large time surface statistics, but one has to further divide into subclasses. Some of the fluctuation laws were first discovered in random matrix models. Moreover, the limit process for curved limit shape turned out to show up in a dynamical version of hermitian random matrices, but this analogy does not extend to the case of symmetric matrices. Therefore the connections between growth models and random matrices is only partial.Comment: 18 pages, 8 figures; Contribution to StatPhys24 special issue; minor corrections in scaling of section 2.

Replica Bethe ansatz derivation of the Tracy-Widom distribution of the free energy fluctuations in one-dimensional directed polymers

The distribution function of the free energy fluctuations in one-dimensional directed polymers with $\delta$-correlated random potential is studied by mapping the replicated problem to the $N$-particle quantum boson system with attractive interactions. We find the full set of eigenfunctions and eigenvalues of this many-body system and perform the summation over the entire spectrum of excited states. It is shown that in the thermodynamic limit the problem is reduced to the Fredholm determinant with the Airy kernel yielding the universal Tracy-Widom distribution, which is known to describe the statistical properties of the Gaussian unitary ensemble as well as many other statistical systems.Comment: 23 page

Discovery of a Variable Star Population in NGC 2808

We have applied the image subtraction method to images of the peculiar, bimodal-horizontal branch globular cluster NGC 2808, taken over a total of six nights over a range of five months. As a result, we have found, for the first time, a sizeable population of variable stars in the crowded inner regions of the cluster, thus raising the known RR Lyrae population in the cluster to a total of 18 stars. In addition, an eclipsing binary and two other variables with periods longer than 1 day were also found. Periods, positions and (differential) light curves are provided for all the detected variables. The Oosterhoff classification of NGC 2808, which has recently been associated with a previously unknown dwarf galaxy in Canis Major, is briefly discussed.Comment: 8 pages, 4 figures. A&A, in pres

NGC 300: an extremely faint, outer stellar disk observed to 10 scale lengths

We have used the Gemini Multi-object Spectrograph (GMOS) on the Gemini South 8m telescope in exceptional conditions (0.6" FWHM seeing) to observe the outer stellar disk of the Sculptor group galaxy NGC 300 at two locations. At our point source detection threshold of r' = 27.0 (3-sigma) mag, we trace the stellar disk out to a radius of 24', or 2.2 R_25 where R_25 is the 25 mag/arcsec**2 isophotal radius. This corresponds to about 10 scale lengths in this low-luminosity spiral (M_B = -18.6), or about 14.4 kpc at a cepheid distance of 2.0 +/- 0.07 Mpc. The background galaxy counts are derived in the outermost field, and these are within 10% of the mean survey counts from both Hubble Deep Fields. The luminosity profile is well described by a nucleus plus a simple exponential profile out to 10 optical scale lengths. We reach an effective surface brightness of 30.5 mag/arcsec**2 (2-sigma) at 55% completeness which doubles the known radial extent of the optical disk. These levels are exceedingly faint in the sense that the equivalent surface brightness in B or V is about 32 mag/arcsec**2. We find no evidence for truncation of the stellar disk. Only star counts can be used to reliably trace the disk to such faint levels, since surface photometry is ultimately limited by nonstellar sources of radiation. In the Appendix, we derive the expected surface brightness of one such source: dust scattering of starlight in the outer disk.Comment: ApJ accepted -- 30 pages, 13 figures -- see ftp://www.aao.gov.au/pub/local/jbh/astro-ph/N300 for full resolution figures and preprin

A Sublinear Variance Bound for Solutions of a Random Hamilton Jacobi Equation

We estimate the variance of the value function for a random optimal control problem. The value function is the solution $w^\epsilon$ of a Hamilton-Jacobi equation with random Hamiltonian $H(p,x,\omega) = K(p) - V(x/\epsilon,\omega)$ in dimension $d \geq 2$. It is known that homogenization occurs as $\epsilon \to 0$, but little is known about the statistical fluctuations of $w^\epsilon$. Our main result shows that the variance of the solution $w^\epsilon$ is bounded by $O(\epsilon/|\log \epsilon|)$. The proof relies on a modified Poincar\'e inequality of Talagrand

Extremal statistics of curved growing interfaces in 1+1 dimensions

We study the joint probability distribution function (pdf) of the maximum M of the height and its position X_M of a curved growing interface belonging to the universality class described by the Kardar-Parisi-Zhang equation in 1+1 dimensions. We obtain exact results for the closely related problem of p non-intersecting Brownian bridges where we compute the joint pdf P_p(M,\tau_M) where \tau_M is there the time at which the maximal height M is reached. Our analytical results, in the limit p \to \infty, become exact for the interface problem in the growth regime. We show that our results, for moderate values of p \sim 10 describe accurately our numerical data of a prototype of these systems, the polynuclear growth model in droplet geometry. We also discuss applications of our results to the ground state configuration of the directed polymer in a random potential with one fixed endpoint.Comment: 6 pages, 4 figures. Published version, to appear in Europhysics Letters. New results added for non-intersecting excursion

M75, a Globular Cluster with a Trimodal Horizontal Branch. I. Color-Magnitude Diagram

Deep UBVI photometry for a large field covering the distant globular cluster M75 (NGC 6864) is presented. We confirm a previous suggestion (Catelan et al. 1998a) that M75 possesses a bimodal horizontal branch (HB) bearing striking resemblance to the well-known case of NGC 1851. In addition, we detect a third, smaller grouping of stars on the M75 blue tail, separated from the bulk of the blue HB stars by a gap spanning about 0.5 mag in V. Such a group of stars may correspond to the upper part of a very extended, though thinly populated, blue tail. Thus M75 appears to have a trimodal HB. The presence of the "Grundahl jump" is verified using the broadband U filter. We explore the color-magnitude diagram of M75 with the purpose of deriving the cluster's fundamental parameters, and find a metallicity of [Fe/H] = -1.03 +/- 0.17 dex and -1.24 +/- 0.21 dex in the Carretta & Gratton (1997) and Zinn & West (1984) scales, respectively. We discuss earlier suggestions that the cluster has an anomalously low ratio of bright red giants to HB stars. A differential age analysis with respect to NGC 1851 suggests that the two clusters are essentially coeval.Comment: 19 pages, 15 figures, emulateapj5/apjfonts style. Astronomical Journal, in press. This version contains some very low-resolution figures, due to the size constraints of astro-ph. We strongly encourage the interested reader to download instead the preprint with full-resolution figures, which can be found at http://www.astro.puc.cl/~mcatelan

A multi-layer extension of the stochastic heat equation

Motivated by recent developments on solvable directed polymer models, we define a 'multi-layer' extension of the stochastic heat equation involving non-intersecting Brownian motions.Comment: v4: substantially extended and revised versio