61 research outputs found
Equilibrium and non-equilibrium Ising models by means of PCA
We propose a unified approach to reversible and irreversible PCA dynamics,
and we show that in the case of 1D and 2D nearest neighbour Ising systems with
periodic boundary conditions we are able to compute the stationary measure of
the dynamics also when the latter is irreversible. We also show how, according
to [DPSS12], the stationary measure is very close to the Gibbs for a suitable
choice of the parameters of the PCA dynamics, both in the reversible and in the
irreversible cases. We discuss some numerical aspects regarding this topic,
including a possible parallel implementation
On the blockage problem and the non-analyticity of the current for the parallel TASEP on a ring
The Totally Asymmetric Simple Exclusion Process (TASEP) is an important
example of a particle system driven by an irreversible Markov chain. In this
paper we give a simple yet rigorous derivation of the chain stationary measure
in the case of parallel updating rule. In this parallel framework we then
consider the blockage problem (aka slow bond problem). We find the exact
expression of the current for an arbitrary blockage intensity in
the case of the so-called rule-184 cellular automaton, i.e. a parallel TASEP
where at each step all particles free-to-move are actually moved. Finally, we
investigate through numerical experiments the conjecture that for parallel
updates other than rule-184 the current may be non-analytic in the blockage
intensity around the value
Regular subgroups with large intersection
In this paper we study the relationships between the elementary abelian
regular subgroups and the Sylow -subgroups of their normalisers in the
symmetric group , in view of the interest that
they have recently raised for their applications in symmetric cryptography
On the statistical description of the inbound air traffic over Heathrow airport
We present a model to describe the inbound air traffic over a congested hub.
We show that this model gives a very accurate description of the traffic by the
comparison of our theoretical distribution of the queue with the actual
distribution observed over Heathrow airport. We discuss also the robustness of
our model
A Chain of Normalizers in the Sylow -subgroups of the symmetric group on letters
On the basis of an initial interest in symmetric cryptography, in the present
work we study a chain of subgroups. Starting from a Sylow -subgroup of
AGL(2,n), each term of the chain is defined as the normalizer of the previous
one in the symmetric group on letters. Partial results and computational
experiments lead us to conjecture that, for large values of , the index of a
normalizer in the consecutive one does not depend on . Indeed, there is a
strong evidence that the sequence of the logarithms of such indices is the one
of the partial sums of the numbers of partitions into at least two distinct
parts
Rigid commutators and a normalizer chain
The novel notion of rigid commutators is introduced to determine the sequence
of the logarithms of the indices of a certain normalizer chain in the Sylow
2-subgroup of the symmetric group on 2^n letters. The terms of this sequence
are proved to be those of the partial sums of the partitions of an integer into
at least two distinct parts, that relates to a famous Euler's partition
theorem
Effects of boundary conditions on irreversible dynamics
We present a simple one-dimensional Ising-type spin system on which we define
a completely asymmetric Markovian single spin-flip dynamics. We study the
system at a very low, yet non-zero, temperature and we show that for empty
boundary conditions the Gibbs measure is stationary for such dynamics, while
introducing in a single site a condition the stationary measure changes
drastically, with macroscopical effects. We achieve this result defining an
absolutely convergent series expansion of the stationary measure around the
zero temperature system. Interesting combinatorial identities are involved in
the proofs
Entropy-driven cutoff phenomena
In this paper we present, in the context of Diaconis' paradigm, a general
method to detect the cutoff phenomenon. We use this method to prove cutoff in a
variety of models, some already known and others not yet appeared in
literature, including a chain which is non-reversible w.r.t. its stationary
measure. All the given examples clearly indicate that a drift towards the
opportune quantiles of the stationary measure could be held responsible for
this phenomenon. In the case of birth- and-death chains this mechanism is
fairly well understood; our work is an effort to generalize this picture to
more general systems, such as systems having stationary measure spread over the
whole state space or systems in which the study of the cutoff may not be
reduced to a one-dimensional problem. In those situations the drift may be
looked for by means of a suitable partitioning of the state space into classes;
using a statistical mechanics language it is then possible to set up a kind of
energy-entropy competition between the weight and the size of the classes.
Under the lens of this partitioning one can focus the mentioned drift and prove
cutoff with relative ease.Comment: 40 pages, 1 figur
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