790 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
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
Testing the irreversibility of a Gibbsian process via hitting and return times
We introduce estimators for the entropy production of a Gibbsian process
based on the observation of a single or two typical trajectories. These
estimators are built with adequate hitting and return times. We then study
their convergence and fluctuation properties. This provides statisticals test
for the irreversibility of Gibbsian processes.Comment: 16 pages; Corrected version; To appear in Nonlinearit
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