Difference between heartwood and sapwood
Forest Products Laboratory (U.S.)
1919
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Comment: Published at http://dx.doi.org/10.1214/009117906000000449 in the
Annals of Probability (http://www.imstat.org/aop/) by the Institute of
Mathematical Statistics (http://www.imstat.org)
In this paper we consider the one-dimensional weakly asymmetric simple exclusion process under the invariant state $\nu_{\rho}$: the Bernoulli product measure of parameter $\rho\in{(0,1)}$. We show that the limit density field is governed by
an Ornstein-Uhlenbeck process for strength asymmetry $n^{2-\gamma}$ if $\gamma\in(1/2,1)$, while for $\gamma=1/2$ it
is an energy solution of the KPZ equation. From this result we obtain that the fluctuations of the current of particles are Gaussian distributed for $\gamma\in(1/2,1)$, while for $\gamma=1/2$ the limit distribution is written in terms of the KPZ equation.
In these notes we use renormalization techniques to derive a second order Boltzmann-Gibbs Principle which allow us to characterize the equilibrium fluctuations of weakly asymmetric exclusion processes as within the KPZ universality class.
Comment: 13 pages, no figures
In this paper we consider an additive functional of an observable $V(x)$ of a
Markov jump process. We assume that the law of the expected jump time $t(x)$
under the invariant probability measure $\pi$ of the skeleton chain belongs to
the domain of attraction of a subordinator. Then, the scaled limit of the
functional is a Mittag-Leffler proces, provided that $\Psi(x):=V(x)t(x)$ is
square integrable w.r.t. $\pi$. When the law of $\Psi(x)$ belongs to a domain
of attraction of a stable law the resulting process can be described by a
composition of a stable process and the inverse of a subordinator and these
processes are not necessarily independent. On the other hand when the
singularities of $\Psi(x)$ and $t(x)$ do not overlap with large probability the
law of the resulting process has some scaling invariance property. We provide
an ap...
Comment: Published by Annales Henri Poincare Volume 13, Number 4 (2012),
813-826
