92 research outputs found
Typical support and Sanov large deviations of correlated states
Discrete stationary classical processes as well as quantum lattice states are
asymptotically confined to their respective typical support, the exponential
growth rate of which is given by the (maximal ergodic) entropy. In the iid case
the distinguishability of typical supports can be asymptotically specified by
means of the relative entropy, according to Sanov's theorem. We give an
extension to the correlated case, referring to the newly introduced class of
HP-states.Comment: 29 pages, no figures, references adde
Exclusion processes with degenerate rates: convergence to equilibrium and tagged particle
Stochastic lattice gases with degenerate rates, namely conservative particle
systems where the exchange rates vanish for some configurations, have been
introduced as simplified models for glassy dynamics. We introduce two
particular models and consider them in a finite volume of size in
contact with particle reservoirs at the boundary. We prove that, as for
non--degenerate rates, the inverse of the spectral gap and the logarithmic
Sobolev constant grow as . It is also shown how one can obtain, via a
scaling limit from the logarithmic Sobolev inequality, the exponential decay of
a macroscopic entropy associated to a degenerate parabolic differential
equation (porous media equation). We analyze finally the tagged particle
displacement for the stationary process in infinite volume. In dimension larger
than two we prove that, in the diffusive scaling limit, it converges to a
Brownian motion with non--degenerate diffusion coefficient.Comment: 25 pages, 3 figure
Minimum memory for generating rare events
We classify the rare events of structured, memoryful stochastic processes and use this to analyze sequential and parallel generators for these events. Given a stochastic process, we introduce a method to construct a process whose typical realizations are a given process' rare events. This leads to an expression for the minimum memory required to generate rare events. We then show that the recently discovered classical-quantum ambiguity of simplicity also occurs when comparing the structure of process fluctuations
Cut Points and Diffusions in Random Environment
In this article we investigate the asymptotic behavior of a new class of
multi-dimensional diffusions in random environment. We introduce cut times in
the spirit of the work done by Bolthausen, Sznitman and Zeitouni, see [4], in
the discrete setting providing a decoupling effect in the process. This allows
us to take advantage of an ergodic structure to derive a strong law of large
numbers with possibly vanishing limiting velocity and a central limit theorem
under the quenched measure.Comment: 44 pages; accepted for publication in "Journal of Theoretical
Probability
Rigorous Probabilistic Analysis of Equilibrium Crystal Shapes
The rigorous microscopic theory of equilibrium crystal shapes has made
enormous progress during the last decade. We review here the main results which
have been obtained, both in two and higher dimensions. In particular, we
describe how the phenomenological Wulff and Winterbottom constructions can be
derived from the microscopic description provided by the equilibrium
statistical mechanics of lattice gases. We focus on the main conceptual issues
and describe the central ideas of the existing approaches.Comment: To appear in the March 2000 special issue of Journal of Mathematical
Physics on Probabilistic Methods in Statistical Physic
Regularity Properties and Pathologies of Position-Space Renormalization-Group Transformations
We reconsider the conceptual foundations of the renormalization-group (RG)
formalism, and prove some rigorous theorems on the regularity properties and
possible pathologies of the RG map. Regarding regularity, we show that the RG
map, defined on a suitable space of interactions (= formal Hamiltonians), is
always single-valued and Lipschitz continuous on its domain of definition. This
rules out a recently proposed scenario for the RG description of first-order
phase transitions. On the pathological side, we make rigorous some arguments of
Griffiths, Pearce and Israel, and prove in several cases that the renormalized
measure is not a Gibbs measure for any reasonable interaction. This means that
the RG map is ill-defined, and that the conventional RG description of
first-order phase transitions is not universally valid. For decimation or
Kadanoff transformations applied to the Ising model in dimension ,
these pathologies occur in a full neighborhood of the low-temperature part of the first-order
phase-transition surface. For block-averaging transformations applied to the
Ising model in dimension , the pathologies occur at low temperatures
for arbitrary magnetic-field strength. Pathologies may also occur in the
critical region for Ising models in dimension . We discuss in detail
the distinction between Gibbsian and non-Gibbsian measures, and give a rather
complete catalogue of the known examples. Finally, we discuss the heuristic and
numerical evidence on RG pathologies in the light of our rigorous theorems.Comment: 273 pages including 14 figures, Postscript, See also
ftp.scri.fsu.edu:hep-lat/papers/9210/9210032.ps.
Reduced Spontaneous Eye Blink Rates in Recreational Cocaine Users: Evidence for Dopaminergic Hypoactivity
Chronic use of cocaine is associated with a reduced density of dopaminergic D2 receptors in the striatum, with negative consequences for cognitive control processes. Increasing evidence suggests that cognitive control is also affected in recreational cocaine consumers. This study aimed at linking these observations to dopaminergic malfunction by studying the spontaneous eyeblink rate (EBR), a marker of striatal dopaminergic functioning, in adult recreational users and a cocaine-free sample that was matched on age, race, gender, and personality traits. Correlation analyses show that EBR is significantly reduced in recreational users compared to cocaine-free controls, suggesting that cocaine use induces hypoactivity in the subcortical dopamine system
Dopamine and inhibitory action control: evidence from spontaneous eye blink rates
The inhibitory control of actions has been claimed to rely on dopaminergic pathways. Given that this hypothesis is mainly based on patient and drug studies, some authors have questioned its validity and suggested that beneficial effects of dopaminergic stimulants on response inhibition may be limited to cases of suboptimal inhibitory functioning. We present evidence that, in carefully selected healthy adults, spontaneous eyeblink rate, a marker of central dopaminergic functioning, reliably predicts the efficiency in inhibiting unwanted action tendencies in a stop-signal task. These findings support the assumption of a modulatory role for dopamine in inhibitory action control
Euclidean Gibbs states of interacting quantum anharmonic oscillators
A rigorous description of the equilibrium thermodynamic properties of an
infinite system of interacting -dimensional quantum anharmonic oscillators
is given. The oscillators are indexed by the elements of a countable set
, possibly irregular; the anharmonic potentials
vary from site to site. The description is based on the representation of the
Gibbs states in terms of path measures -- the so called Euclidean Gibbs
measures. It is proven that: (a) the set of such measures
is non-void and compact; (b) every obeys an
exponential integrability estimate, the same for the whole set
; (c) every has a
Lebowitz-Presutti type support; (d) is a singleton at
high temperatures. In the case of attractive interaction and we prove
that at low temperatures. The uniqueness of Gibbs
measures due to quantum effects and at a nonzero external field are also proven
in this case. Thereby, a qualitative theory of phase transitions and quantum
effects, which interprets most important experimental data known for the
corresponding physical objects, is developed. The mathematical result of the
paper is a complete description of the set , which refines
and extends the results known for models of this type.Comment: 60 page
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