1,224 research outputs found
Propagation of Chaos for a Balls into Bins Model
Consider a finite number of balls initially placed in bins. At each time
step a ball is taken from each non-empty bin. Then all the balls are uniformly
reassigned into bins. This finite Markov chain is called Repeated
Balls-into-Bins process and is a discrete time interacting particle system with
parallel updating. We prove that, starting from a suitable (chaotic) set of
initial states, as , the numbers of balls in each bin becomes
independent from the rest of the system i.e. we have propagation of chaos. We
furthermore study some equilibrium properties of the limiting nonlinear
process
Relaxation time of -reversal chains and other chromosome shuffles
We prove tight bounds on the relaxation time of the so-called -reversal
chain, which was introduced by R. Durrett as a stochastic model for the
evolution of chromosome chains. The process is described as follows. We have
distinct letters on the vertices of the -cycle ( mod
); at each step, a connected subset of the graph is chosen uniformly at
random among all those of length at most , and the current permutation is
shuffled by reversing the order of the letters over that subset. We show that
the relaxation time , defined as the inverse of the spectral gap of
the associated Markov generator, satisfies . Our results can be interpreted as strong evidence for a
conjecture of R. Durrett predicting a similar behavior for the mixing time of
the chain.Comment: Published at http://dx.doi.org/10.1214/105051606000000295 in the
Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute
of Mathematical Statistics (http://www.imstat.org
Kinetically constrained spin models
We analyze the density and size dependence of the relaxation time for
kinetically constrained spin models (KCSM) intensively studied in the physical
literature as simple models sharing some of the features of a glass transition.
KCSM are interacting particle systems on with Glauber-like dynamics,
reversible w.r.t. a simple product i.i.d Bernoulli() measure. The essential
feature of a KCSM is that the creation/destruction of a particle at a given
site can occur only if the current configuration of empty sites around it
satisfies certain constraints which completely define each specific model. No
other interaction is present in the model. From the mathematical point of view,
the basic issues concerning positivity of the spectral gap inside the
ergodicity region and its scaling with the particle density remained open
for most KCSM (with the notably exception of the East model in
\cite{Aldous-Diaconis}). Here for the first time we: i) identify the ergodicity
region by establishing a connection with an associated bootstrap percolation
model; ii) develop a novel multi-scale approach which proves positivity of the
spectral gap in the whole ergodic region; iii) establish, sometimes optimal,
bounds on the behavior of the spectral gap near the boundary of the ergodicity
region and iv) establish pure exponential decay for the persistence function.
Our techniques are flexible enough to allow a variety of constraints and our
findings disprove certain conjectures which appeared in the physical literature
on the basis of numerical simulations
Molecular detection of Rickettsia, Borrelia, and Babesia species in Ixodes ricinus sampled in northeastern, central, and insular areas of Italy.
The aim of the present study was to provide insight into the diversity of tick-borne pathogens circulating in Italy, carried/transmitted by Ixodes ricinus, one of the most abundant tick species in the country. A total of 447 specimens sampled in five areas of northeastern, central and insular Italy were analysed by polymerase chain reaction and sequencing for the presence of rickettsiae, borreliae and babesiae. Several rickettsial species of the spotted fever group of zoonotic concern and other zoonotic pathogens were found, such as Borrelia burgdorferi s.s., Borrelia afzelii, Borrelia garinii, and Babesia venatorum. These findings confirm a wide distribution of tick-borne bacterial and protozoan species in Italy, and highlight the sanitary importance of I. ricinus, often recorded as feeding on humans
L'esecuzione nei contratti di appalto di opere pubbliche
Viene decritta la normativa relativa alla gestione del contratto d'appalto pubblico a sèguito delle riforme operate dal III Decreto correttivo e dal Decreto di recepimento della cd. Direttiva Ricorsi
Propagation of chaos for a General Balls into Bins dynamics
Consider balls initially placed in bins. At each time step take a
ball from each non-empty bin and \emph{randomly} reassign the balls into the
bins.We call this finite Markov chain \emph{General Repeated Balls into Bins}
process. It is a discrete time interacting particles system with parallel
updates. Assuming a \emph{quantitative} chaotic condition on the reassignment
rule we prove a \emph{quantitative} propagation of chaos for this model. We
furthermore study some equilibrium properties of the limiting nonlinear
process
On the dynamical behavior of the ABC model
We consider the ABC dynamics, with equal density of the three species, on the
discrete ring with sites. In this case, the process is reversible with
respect to a Gibbs measure with a mean field interaction that undergoes a
second order phase transition. We analyze the relaxation time of the dynamics
and show that at high temperature it grows at most as while it grows at
least as at low temperature
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