1,075 research outputs found
Censored Glauber Dynamics for the mean field Ising Model
We study Glauber dynamics for the Ising model on the complete graph on
vertices, known as the Curie-Weiss Model. It is well known that at high
temperature () the mixing time is , whereas at low
temperature () it is . Recently, Levin, Luczak and
Peres considered a censored version of this dynamics, which is restricted to
non-negative magnetization. They proved that for fixed , the
mixing-time of this model is , analogous to the
high-temperature regime of the original dynamics. Furthermore, they showed
\emph{cutoff} for the original dynamics for fixed . The question
whether the censored dynamics also exhibits cutoff remained unsettled.
In a companion paper, we extended the results of Levin et al. into a complete
characterization of the mixing-time for the Currie-Weiss model. Namely, we
found a scaling window of order around the critical temperature
, beyond which there is cutoff at high temperature. However,
determining the behavior of the censored dynamics outside this critical window
seemed significantly more challenging.
In this work we answer the above question in the affirmative, and establish
the cutoff point and its window for the censored dynamics beyond the critical
window, thus completing its analogy to the original dynamics at high
temperature. Namely, if for some with
, then the mixing-time has order . The cutoff constant is , where is the unique positive root of
, and the cutoff window has order .Comment: 55 pages, 4 figure
Moderate deviations for random field Curie-Weiss models
The random field Curie-Weiss model is derived from the classical Curie-Weiss
model by replacing the deterministic global magnetic field by random local
magnetic fields. This opens up a new and interestingly rich phase structure. In
this setting, we derive moderate deviations principles for the random total
magnetization , which is the partial sum of (dependent) spins. A typical
result is that under appropriate assumptions on the distribution of the local
external fields there exist a real number , a positive real number
, and a positive integer such that satisfies
a moderate deviations principle with speed and rate
function , where .Comment: 21 page
Immunological studies on the light-harvesting polypeptides of photosystems I and II
AbstractMonoclonal and polyclonal antibodies have been raised against the three apoproteins of the peripheral light-harvesting complex of photosystem I (LHC I) from Pisum sativum L. These antibodies have been used to study the immunological relatedness of the light-harvesting polypeptides of photosystems I and II. The results suggest that there is no immunological/structural relationship between the two light-harvesting systems. The apoproteins of the LHC I fall into two distinct groups corresponding to the two chlorophyllab complexes comprising the PS I antenna
Mod-Gaussian convergence and its applications for models of statistical mechanics
In this paper we complete our understanding of the role played by the
limiting (or residue) function in the context of mod-Gaussian convergence. The
question about the probabilistic interpretation of such functions was initially
raised by Marc Yor. After recalling our recent result which interprets the
limiting function as a measure of "breaking of symmetry" in the Gaussian
approximation in the framework of general central limit theorems type results,
we introduce the framework of -mod-Gaussian convergence in which the
residue function is obtained as (up to a normalizing factor) the probability
density of some sequences of random variables converging in law after a change
of probability measure. In particular we recover some celebrated results due to
Ellis and Newman on the convergence in law of dependent random variables
arising in statistical mechanics. We complete our results by giving an
alternative approach to the Stein method to obtain the rate of convergence in
the Ellis-Newman convergence theorem and by proving a new local limit theorem.
More generally we illustrate our results with simple models from statistical
mechanics.Comment: 49 pages, 21 figure
Asymptotics of the mean-field Heisenberg model
We consider the mean-field classical Heisenberg model and obtain detailed
information about the total spin of the system by studying the model on a
complete graph and sending the number of vertices to infinity. In particular,
we obtain Cramer- and Sanov-type large deviations principles for the total spin
and the empirical spin distribution and demonstrate a second-order phase
transition in the Gibbs measures. We also study the asymptotics of the total
spin throughout the phase transition using Stein's method, proving central
limit theorems in the sub- and supercritical phases and a nonnormal limit
theorem at the critical temperature.Comment: 44 page
Principle of Balance and the Sea Content of the Proton
In this study, the proton is taken as an ensemble of quark-gluon Fock states.
Using the principle of balance that every Fock state should be balanced with
all of the nearby Fock states (denoted as the balance model), instead of the
principle of detailed balance that any two nearby Fock states should be
balanced with each other (denoted as the detailed balance model), the
probabilities of finding every Fock state of the proton are obtained. The
balance model can be taken as a revised version of the detailed balance model,
which can give an excellent description of the light flavor sea asymmetry
(i.e., ) without any parameter. In case of
sub-processes not considered, the balance model and the
detailed balance model give the same results. In case of
sub-processes considered, there is about 10 percent difference between the
results of these models. We also calculate the strange content of the proton
using the balance model under the equal probability assumption.Comment: 32 latex pages, 4 ps figures, to appear in PR
Fluctuation Theorems for Entropy Production and Heat Dissipation in Periodically Driven Markov Chains
Asymptotic fluctuation theorems are statements of a Gallavotti-Cohen symmetry
in the rate function of either the time-averaged entropy production or heat
dissipation of a process. Such theorems have been proved for various general
classes of continuous-time deterministic and stochastic processes, but always
under the assumption that the forces driving the system are time independent,
and often relying on the existence of a limiting ergodic distribution. In this
paper we extend the asymptotic fluctuation theorem for the first time to
inhomogeneous continuous-time processes without a stationary distribution,
considering specifically a finite state Markov chain driven by periodic
transition rates. We find that for both entropy production and heat
dissipation, the usual Gallavotti-Cohen symmetry of the rate function is
generalized to an analogous relation between the rate functions of the original
process and its corresponding backward process, in which the trajectory and the
driving protocol have been time-reversed. The effect is that spontaneous
positive fluctuations in the long time average of each quantity in the forward
process are exponentially more likely than spontaneous negative fluctuations in
the backward process, and vice-versa, revealing that the distributions of
fluctuations in universes in which time moves forward and backward are related.
As an additional result, the asymptotic time-averaged entropy production is
obtained as the integral of a periodic entropy production rate that generalizes
the constant rate pertaining to homogeneous dynamics
The Nature of Star Formation in Lensed Galaxies at High Redshift
We present near-infrared photometry of all available gravitationally lensed ‘arcs’ with spectroscopic redshifts. By combining this photometry with optical data, we find that the bulk of the systems with z ~ 1 are intrinsically blue across the rest-frame spectral region 2000 Å to 1 μm. Using a combination of optical and optical-infrared colours, we demonstrate that these systems cannot be blue by virtue of a secondary burst of star formation superimposed on an evolved population, but we are unable to distinguish directly between major star formation events in a generic young galaxy and an extended era of constant star formation typical of late-type spirals. Using various arguments, we conclude that our arcs represent modest gravitational magnification of typical field galaxies. Consequently, if the star formation seen is representative of that in field galaxies at z ≥ 1, the absence of high-redshift galaxies in current deep spectroscopic surveys to bJ≃24bJ≃24 supports the hypothesis that the bulk of the star formation in normal galaxies occurred over an extended era up to the epoch corresponding to z ~ 1
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