113 research outputs found
Stochastic Ising model with flipping sets of spins and fast decreasing temperature
This paper deals with the stochastic Ising model with a temperature shrinking
to zero as time goes to infinity. A generalization of the Glauber dynamics is
considered, on the basis of the existence of simultaneous flips of some spins.
Such dynamics act on a wide class of graphs which are periodic and embedded in
. The interactions between couples of spins are assumed to be
quenched i.i.d. random variables following a Bernoulli distribution with
support . The specific problem here analyzed concerns the assessment
of how often (finitely or infinitely many times, almost surely) a given spin
flips. Adopting the classification proposed in \cite{GNS}, we present
conditions in order to have models of type (any spin flips
finitely many times), (any spin flips infinitely many times) and
(a mixed case). Several examples are provided in all dimensions
and for different cases of graphs. The most part of the obtained results holds
true for the case of zero-temperature and some of them for the cubic lattice
as well.Comment: 31 pages, 6 figures, Accepted for publication in "Annales de
l'Institut Henri Poincar\'e, Probabilit\'es et Statistiques
One-dimensional infinite memory imitation models with noise
In this paper we study stochastic process indexed by
constructed from certain transition kernels depending on the whole past. These
kernels prescribe that, at any time, the current state is selected by looking
only at a previous random instant. We characterize uniqueness in terms of
simple concepts concerning families of stochastic matrices, generalizing the
results previously obtained in De Santis and Piccioni (J. Stat. Phys.,
150(6):1017--1029, 2013).Comment: 22 pages, 3 figure
Perfect simulation of autoregressive models with infinite memory
In this paper we consider the problem of determining the law of binary
stochastic processes from transition kernels depending on the whole past. These
kernels are linear in the past values of the process. They are allowed to
assume values close to both 0 and 1, preventing the application of usual
results on uniqueness. More precisely we give sufficient conditions for
uniqueness and non-uniqueness. In the former case a perfect simulation
algorithm is also given.Comment: 12 page
Convergence in Energy-Lowering (Disordered) Stochastic Spin Systems
We consider stochastic processes, S^t \equiv (S_x^t : x \in Z^d), with each
S_x^t taking values in some fixed finite set, in which spin flips (i.e.,
changes of S_x^t) do not raise the energy. We extend earlier results of
Nanda-Newman-Stein that each site x has almost surely only finitely many flips
that strictly lower the energy and thus that in models without zero-energy
flips there is convergence to an absorbing state. In particular, the assumption
of finite mean energy density can be eliminated by constructing a
percolation-theoretic Lyapunov function density as a substitute for the mean
energy density. Our results apply to random energy functions with a
translation-invariant distribution and to quite general (not necessarily
Markovian) dynamics.Comment: 11 page
Relations Between Stochastic Orderings and generalized Stochastic Precedence
The concept of "stochastic precedence" between two real-valued random
variables has often emerged in different applied frameworks. In this paper we
consider a slightly more general, and completely natural, concept of stochastic
precedence and analyze its relations with the notions of stochastic ordering.
Such a study leads us to introducing some special classes of bivariate copulas.
Motivations for our study can arise from different fields. In particular we
consider the frame of Target-Based Approach in decisions under risk. This
approach has been mainly developed under the assumption of stochastic
independence between "Prospects" and "Targets". Our analysis concerns the case
of stochastic dependence.Comment: 13 pages, 6 figure
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