The Kac limit for finite-range spin glasses

We consider a finite range spin glass model in arbitrary dimension, where the strength of the two-body coupling decays to zero over some distance $\gamma^{-1}$. We show that, under mild assumptions on the interaction potential, the infinite-volume free energy of the system converges to that of the Sherrington-Kirkpatrick one, in the Kac limit $\gamma\to0$. This could be a first step toward an expansion around mean field theory, for spin glass systems.Comment: 4 pages; references updated, typos correcte

Monotonicity and Thermodynamic Limit for Short Range Disordered Models

If the variance of a short range Gaussian random potential grows like the volume its quenched thermodynamic limit is reached monotonically.Comment: 2 references adde

Nonergodicity and Central Limit Behavior for Long-range Hamiltonians

We present a molecular dynamics test of the Central Limit Theorem (CLT) in a paradigmatic long-range-interacting many-body classical Hamiltonian system, the HMF model. We calculate sums of velocities at equidistant times along deterministic trajectories for different sizes and energy densities. We show that, when the system is in a chaotic regime (specifically, at thermal equilibrium), ergodicity is essentially verified, and the Pdfs of the sums appear to be Gaussians, consistently with the standard CLT. When the system is, instead, only weakly chaotic (specifically, along longstanding metastable Quasi-Stationary States), nonergodicity (i.e., discrepant ensemble and time averages) is observed, and robust $q$-Gaussian attractors emerge, consistently with recently proved generalizations of the CLT.Comment: 6 pages 7 figures. Improved version accepted for publication on Europhysics Letter

Multivariate limit theorems in the context of long-range dependence

We study the limit law of a vector made up of normalized sums of functions of long-range dependent stationary Gaussian series. Depending on the memory parameter of the Gaussian series and on the Hermite ranks of the functions, the resulting limit law may be (a) a multivariate Gaussian process involving dependent Brownian motion marginals, or (b) a multivariate process involving dependent Hermite processes as marginals, or (c) a combination. We treat cases (a), (b) in general and case (c) when the Hermite components involve ranks 1 and 2. We include a conjecture about case (c) when the Hermite ranks are arbitrary

The southernmost range limit for the hidden angelshark Squatina occulta

Background: Angelsharks (Genus Squatina) are distributed in the southern Southwest Atlantic Ocean between southeastern Brazil and central Patagonia. The endangered hidden angelshark Squatina occulta is reported in the literature as ranging from Espírito Santo, Brazil to Southern Uruguay. Its presence in Argentine waters has been suspected but not verified so far. This study describes and analyzes a specimen of S. occulta found in Puerto Quequén 38° 40′S - 58° 50′W, Buenos Aires Province, Argentina. Results: An immature male of 578 mm total length and 1,450 g was collected from commercial landings of the bottom trawl fishery of Puerto Quequén. The specimen exhibited the coloration pattern, dermal denticle distribution, and tooth formula characteristic of S. occulta. Conclusions: Squatina guggenheim and S. argentina are already known to occur off Puerto Quequén. The present finding confirms the presence of a third species of angelshark in Argentina and constitutes the southernmost record of S. occulta.Fil: Estalles, María Lourdes. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata. Instituto de Investigaciones Marinas y Costeras. Universidad Nacional de Mar del Plata. Facultad de Ciencia Exactas y Naturales. Instituto de Investigaciones Marinas y Costeras; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Museo Argentino de Ciencias Naturales ; ArgentinaFil: Chiaramonte, Gustavo Enrique. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Museo Argentino de Ciencias Naturales ; ArgentinaFil: Faria, Vicente V.. Universidade Federal do Ceará; BrasilFil: Luzzatto, Diego. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Museo Argentino de Ciencias Naturales ; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata. Instituto de Investigaciones Marinas y Costeras. Universidad Nacional de Mar del Plata. Facultad de Ciencia Exactas y Naturales. Instituto de Investigaciones Marinas y Costeras; ArgentinaFil: Díaz de Astarloa, Juan Martín. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata. Instituto de Investigaciones Marinas y Costeras. Universidad Nacional de Mar del Plata. Facultad de Ciencia Exactas y Naturales. Instituto de Investigaciones Marinas y Costeras; Argentin

Nonstandard limit theorem for infinite variance functionals

We consider functionals of long-range dependent Gaussian sequences with infinite variance and obtain nonstandard limit theorems. When the long-range dependence is strong enough, the limit is a Hermite process, while for weaker long-range dependence, the limit is $\alpha$-stable L\'{e}vy motion. For the critical value of the long-range dependence parameter, the limit is a sum of a Hermite process and $\alpha$-stable L\'{e}vy motion.Comment: Published in at http://dx.doi.org/10.1214/07-AOP345 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Chaos suppression in the large size limit for long-range systems

We consider the class of long-range Hamiltonian systems first introduced by Anteneodo and Tsallis and called the alpha-XY model. This involves N classical rotators on a d-dimensional periodic lattice interacting all to all with an attractive coupling whose strength decays as r^{-alpha}, r being the distances between sites. Using a recent geometrical approach, we estimate for any d-dimensional lattice the scaling of the largest Lyapunov exponent (LLE) with N as a function of alpha in the large energy regime where rotators behave almost freely. We find that the LLE vanishes as N^{-kappa}, with kappa=1/3 for alpha/d between 0 and 1/2 and kappa=2/3(1-alpha/d) for alpha/d between 1/2 and 1. These analytical results present a nice agreement with numerical results obtained by Campa et al., including deviations at small N.Comment: 10 pages, 3 eps figure