9,707 research outputs found
Markov two-components processes
We propose Markov two-components processes (M2CP) as a probabilistic model of
asynchronous systems based on the trace semantics for concurrency. Considering
an asynchronous system distributed over two sites, we introduce concepts and
tools to manipulate random trajectories in an asynchronous framework: stopping
times, an Asynchronous Strong Markov property, recurrent and transient states
and irreducible components of asynchronous probabilistic processes. The
asynchrony assumption implies that there is no global totally ordered clock
ruling the system. Instead, time appears as partially ordered and random. We
construct and characterize M2CP through a finite family of transition matrices.
M2CP have a local independence property that guarantees that local components
are independent in the probabilistic sense, conditionally to their
synchronization constraints. A synchronization product of two Markov chains is
introduced, as a natural example of M2CP.Comment: 34 page
A cut-invariant law of large numbers for random heaps
Heap monoids equipped with Bernoulli measures are a model of probabilistic
asynchronous systems. We introduce in this framework the notion of asynchronous
stopping time, which is analogous to the notion of stopping time for classical
probabilistic processes. A Strong Bernoulli property is proved. A notion of
cut-invariance is formulated for convergent ergodic means. Then a version of
the Strong law of large numbers is proved for heap monoids with Bernoulli
measures. Finally, we study a sub-additive version of the Law of large numbers
in this framework based on Kingman sub-additive Ergodic Theorem.Comment: 29 pages, 3 figures, 21 reference
Markovian dynamics of concurrent systems
Monoid actions of trace monoids over finite sets are powerful models of
concurrent systems---for instance they encompass the class of 1-safe Petri
nets. We characterise Markov measures attached to concurrent systems by
finitely many parameters with suitable normalisation conditions. These
conditions involve polynomials related to the combinatorics of the monoid and
of the monoid action. These parameters generalise to concurrent systems the
coefficients of the transition matrix of a Markov chain.
A natural problem is the existence of the uniform measure for every
concurrent system. We prove this existence under an irreducibility condition.
The uniform measure of a concurrent system is characterised by a real number,
the characteristic root of the action, and a function of pairs of states, the
Parry cocyle. A new combinatorial inversion formula allows to identify a
polynomial of which the characteristic root is the smallest positive root.
Examples based on simple combinatorial tilings are studied.Comment: 35 pages, 6 figures, 33 reference
On the stochastic calculus method for spins systems
In this note we show how to generalize the stochastic calculus method
introduced by Comets and Neveu [Comm. Math. Phys. 166 (1995) 549-564] for two
models of spin glasses, namely, the SK model with external field and the
perceptron model. This method allows to derive quite easily some fluctuation
results for the free energy in those two cases.Comment: Published at http://dx.doi.org/10.1214/009117904000000919 in the
Annals of Probability (http://www.imstat.org/aop/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Asymptotic Estimates for Perturbed Scaiar Curvature Equation
We have an idea on the influence of a nonlinear term (tending to 0) on the
prescribed scalar curvature equation to have an uniform estimate.Comment: 7 page
Harnack Inequalities for Yamabe Type Equations
We give some a priori estimates of type sup*inf for Yamabe and prescribed
scalar curvature type equations on Riemannian manifolds of dimension >2. The
product sup*inf is caracteristic of those equations, like the usual Harnack
inequalities for non negative harmonic functions. First, we have a lower bound
for sup*inf for some classes of PDE on compact manifolds (like prescribed
scalar cuvature). We also have an upper bound for the same product but on any
Riemannian manifold not necessarily compact. An application of those result is
an uniqueness solution for some PDE.Comment: 16 page
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