7,834 research outputs found
Variational Bounds for the Generalized Random Energy Model
We compute the pressure of the random energy model (REM) and generalized
random energy model(GREM) by establishing variational upper and lower bounds.
For the upper bound, we generalize Guerra's ``broken replica symmetry
bounds",and identify the random probability cascade as the appropriate random
overlap structure for the model. For the REM the lower bound is obtained, in
the high temperature regime using Talagrand's concentration of measure
inequality, and in the low temperature regime using convexity and the high
temperature formula. The lower bound for the GREM follows from the lower bound
for the REM by induction. While the argument for the lower bound is fairly
standard, our proof of the upper bound is new.Comment: 24 page
Spin-Glass Stochastic Stability: a Rigorous Proof
We prove the property of stochastic stability previously introduced as a
consequence of the (unproved) continuity hypothesis in the temperature of the
spin-glass quenched state. We show that stochastic stability holds in
beta-average for both the Sherrington-Kirkpatrick model in terms of the square
of the overlap function and for the Edwards-Anderson model in terms of the bond
overlap. We show that the volume rate at which the property is reached in the
thermodynamic limit is V^{-1}. As a byproduct we show that the stochastic
stability identities coincide with those obtained with a different method by
Ghirlanda and Guerra when applyed to the thermal fluctuations only.Comment: 12 pages, revised versio
Ergodic Properties of Microcanonical Observables
The problem of the existence of a Strong Stochasticity Threshold in the
FPU-beta model is reconsidered, using suitable microcanonical observables of
thermodynamic nature, like the temperature and the specific heat. Explicit
expressions for these observables are obtained by exploiting rigorous methods
of differential geometry. Measurements of the corresponding temporal
autocorrelation functions locate the threshold at a finite value of the energy
density, that results to be indipendent of the number of degrees of freedom.Comment: 19 pages, 6 figure
The Ghirlanda-Guerra Identities
If the variance of a Gaussian spin-glass Hamiltonian grows like the volume
the model fulfills the Ghirlanda-Guerra identities in terms of the normalized
Hamiltonian covariance.Comment: 18 page
Thermodynamic Limit for Mean-Field Spin Models
If the Boltzmann-Gibbs state of a mean-field -particle system
with Hamiltonian verifies the condition for every decomposition , then its free
energy density increases with . We prove such a condition for a wide class
of spin models which includes the Curie-Weiss model, its p-spin generalizations
(for both even and odd p), its random field version and also the finite pattern
Hopfield model. For all these cases the existence of the thermodynamic limit by
subadditivity and boundedness follows.Comment: 15 pages, few improvements. To appear in MPE
The challenges of participatory research with 'tech-savvy' youth
This paper focuses on participatory research and how it can be understood and employed when researching children and youth. The aim of this paper is to provide a theoretically and empirically grounded discussion of participatory research methodologies with respect to investigating the dynamic and evolving phenomenon of young people growing up in networked societies. Initially, we review the nature of participatory research and how other researchers have endeavoured to involve young people (children and youth) in their research projects. Our review of these approaches aims to elucidate what we see as recurring and emerging issues with respect to the methodological design of involving young people as co-researchers. In the light of these issues and in keeping with our aim, we offer a case study of our own research project that seeks to understand the ways in which high school students use new media and network ICT systems (Internet, mobile phone applications, social networking sites) to construct identities, form social relations, and engage in creative practices as part of their everyday lives. The article concludes by offering an assessment of our tripartite model of participatory research that may benefit other researchers who share a similar interest in youth and new media
Matching with shift for one-dimensional Gibbs measures
We consider matching with shifts for Gibbsian sequences. We prove that the
maximal overlap behaves as , where is explicitly identified in
terms of the thermodynamic quantities (pressure) of the underlying potential.
Our approach is based on the analysis of the first and second moment of the
number of overlaps of a given size. We treat both the case of equal sequences
(and nonzero shifts) and independent sequences.Comment: Published in at http://dx.doi.org/10.1214/08-AAP588 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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