A universality property for last-passage percolation paths close to the axis

We consider a last-passage directed percolation model in $Z_+^2$, with i.i.d. weights whose common distribution has a finite $(2+p)$th moment. We study the fluctuations of the passage time from the origin to the point $\big(n,n^{\lfloor a \rfloor}\big)$. We show that, for suitable $a$ (depending on $p$), this quantity, appropriately scaled, converges in distribution as $n\to\infty$ to the Tracy-Widom distribution, irrespective of the underlying weight distribution. The argument uses a coupling to a Brownian directed percolation problem and the strong approximation of Koml\'os, Major and Tusn\'ady.Comment: 8 page

Standing waves of the complex Ginzburg-Landau equation

We prove the existence of nontrivial standing wave solutions of the complex Ginzburg-Landau equation $\phi_t = e^{i\theta} \Delta \phi + e^{i\gamma} |\phi |^\alpha \phi$ with periodic boundary conditions. Our result includes all values of $\theta$ and $\gamma$ for which $\cos \theta \cos \gamma >0$, but requires that $\alpha >0$ be sufficiently small

Creep motion of an elastic string in a random potential

We study the creep motion of an elastic string in a two dimensional pinning landscape by Langevin dynamics simulations. We find that the Velocity-Force characteristics are well described by the creep formula predicted from phenomenological scaling arguments. We analyze the creep exponent $\mu$, and the roughness exponent $\zeta$. Two regimes are identified: when the temperature is larger than the strength of the disorder we find $\mu \approx 1/4$ and $\zeta \approx 2/3$, in agreement with the quasi-equilibrium-nucleation picture of creep motion; on the contrary, lowering enough the temperature, the values of $\mu$ and $\zeta$ increase showing a strong violation of the latter picture.Comment: 4 pages, 3 figure

Non-equilibrium relaxation of an elastic string in random media

We study the relaxation of an elastic string in a two dimensional pinning landscape using Langevin dynamics simulations. The relaxation of a line, initially flat, is characterized by a growing length, $L(t)$, separating the equilibrated short length scales from the flat long distance geometry that keep memory of the initial condition. We find that, in the long time limit, $L(t)$ has a non--algebraic growth, consistent with thermally activated jumps over barriers with power law scaling, $U(L) \sim L^\theta$.Comment: 2 pages, 1 figure, Proceedings of ECRYS-2005 International Workshop on Electronic Crysta

Taxonomic revision and phylogeny of the Ophiocoma brevipes group (Echinodermata, Ophiuroidea) : with description of a new subgenus (Breviturma) and a new species

The taxonomy of the genus Ophiocoma was last revised by Devaney in 1970. Recent discoveries of new species and re-instatement of previously synonymized names suggest that we still do not fully understand the species limits in this genus. A recent biodiversity survey of the SW Indian Ocean shallow reefs strongly suggested an unrecognised species in the genus, closely related to O. brevipes/O. dentata. This study examined both the molecular phylogenetic relationships and the morphological characteristics of several species in the genus in order to characterise the unrecognised species. The focal species clusters with O. brevipes, O. dentata, O. doederleini within a monophyletic clade supported by molecular data for the first time. The name Breviturma subgen. nov. is proposed for this clade, previously known as brevipes group. Type material of nominal species that have been synonymized with O. dentata was examined and re-assessed. Ophiocoma marmorata proved not conspecific with O. dentata. A rarely used character, dorsal disc granule density, was tested and showed differences between the examined species at similar sizes. In combination with colour pattern, disc granule density, arm spine sequence and maximum disc size, the new species was delimited morphologically and described as Ophiocoma krohi sp. nov

An Empirical Study of Price Dispersion in Homogenous Goods Markets

This paper presents the results of an empirical study of price dispersion in homogeneous goods markets. Modern economic theory suggests that inevitable asymmetries of information in markets lead to an equilibrium in which price dispersion is present even when goods are perfectly homogenous. In this paper we present an empirical analysis in which we employ both cross-sectional and time-series data gathered directly from Pricegrabber.com, one of the most popular and comprehensive online shopping/price-comparison sites on the Internet. In particular our analysis focuses on (i) the effect that the number of firms offering a good has on price dispersion, (ii) the informational value to the consumer of using the Pricegrabber website, and (iii) the persistency of price dispersion over time.E-commerce, Internet marketing, Price dispersion, Signaling, Search Cost, Gatekeepers, Regression and other statistical techniques JEL Classification: L81, L86, L11