915 research outputs found
Organized versus self-organized criticality in the abelian sandpile model
We define stabilizability of an infinite volume height configuration and of a
probability measure on height configurations. We show that for high enough
densities, a probability measure cannot be stabilized. We also show that in
some sense the thermodynamic limit of the uniform measures on the recurrent
configurations of the abelian sandpile model (ASM) is a maximal element of the
set of stabilizable measures. In that sense the self-organized critical
behavior of the ASM can be understood in terms of an ordinary transition
between stabilizable and non-stabilizableComment: 17 pages, appeared in Markov Processes and Related Fields 200
Transformations of one-dimensional Gibbs measures with infinite range interaction
We study single-site stochastic and deterministic transforma- tions of
one-dimensional Gibbs measures in the uniqueness regime with infinite-range
interactions. We prove conservation of Gibbsianness and give quantitative
estimates on the decay of the transformed potential. As examples, we consider
exponentially decaying potentials, and potentials decaying as a power-law
Weak coupling limits in a stochastic model of heat conduction
We study the Brownian momentum process, a model of heat conduction, weakly
coupled to heat baths. In two different settings of weak coupling to the heat
baths, we study the non-equilibrium steady state and its proximity to the local
equilibrium measure in terms of the strength of coupling. For three and four
site systems, we obtain the two-point correlation function and show it is
generically not multilinear.Comment: 18 page
Loss without recovery of Gibbsianness during diffusion of continuous spins
We consider a specific continuous-spin Gibbs distribution for a
double-well potential that allows for ferromagnetic ordering. We study the
time-evolution of this initial measure under independent diffusions. For `high
temperature' initial measures we prove that the time-evoved measure
is Gibbsian for all . For `low temperature' initial measures we prove that
stays Gibbsian for small enough times , but loses its Gibbsian
character for large enough . In contrast to the analogous situation for
discrete-spin Gibbs measures, there is no recovery of the Gibbs property for
large in the presence of a non-vanishing external magnetic field. All of
our results hold for any dimension . This example suggests more
generally that time-evolved continuous-spin models tend to be non-Gibbsian more
easily than their discrete-spin counterparts
Large deviations for quantum spin systems
We consider high temperature KMS states for quantum spin systems on a
lattice. We prove a large deviation principle for the distribution of empirical
averages , where the 's are
copies of a self-adjoint element (level one large deviations). From the
analyticity of the generating function, we obtain the central limit theorem. We
generalize to a level two large deviation principle for the distribution of
.Comment: 22 page
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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