Correction. Central limit theorems for additive functionals of the simple exclusion process

Correction to Annals of Probability 28 (2000) 277--302 [doi:10.1214/aop/1019160120].Comment: Published at http://dx.doi.org/10.1214/009117905000000521 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

On microscopic derivation of a fractional stochastic Burgers equation

We derive from a class of microscopic asymmetric interacting particle systems on ${\mathbb Z}$, with long range jump rates of order $|\cdot|^{-(1+\alpha)}$ for $0<\alpha<2$, different continuum fractional SPDEs. More specifically, we show the equilibrium fluctuations of the hydrodynamics mass density field of zero-range processes, depending on the stucture of the asymmetry, and whether the field is translated with process characteristics velocity, is governed in various senses by types of fractional stochastic heat or Burgers equations. The main result: Suppose the jump rate is such that its symmetrization is long range but its (weak) asymmetry is nearest-neighbor. Then, when $\alpha<3/2$, the fluctuation field in space-time scale $1/\alpha:1$, translated with process characteristic velocity, irrespective of the strength of the asymmetry, converges to a fractional stochastic heat equation, the limit also for the symmetric process. However, when $\alpha\geq 3/2$ and the strength of the weak asymmetry is tuned in scale $1-3/2\alpha$, the associated limit points satisfy a martingale formulation of a fractional stochastic Burgers equation.Comment: 24 page

The Role of Women?s Empowerment and Domestic Violence in Child Growth and Undernutrition in a Tribal and Rural Community in South India

Moderate undernutrition continues to affect 46 per cent of children under 5 years of age and 47 per cent of rural women in India. Women?s lack of empowerment is believed to be an important factor in the persistent prevalence of undernutrition. In India, women?s empowerment often varies by community, with tribes sometimes being the most progressive. This paper explores the relationship between women?s empowerment, domestic violence, maternal nutritional status, and the nutritional status and growth over six months in children aged 6 to 24 months in a rural and tribal community. This longitudinal observational study undertaken in rural Karnataka, India included tribal and rural subjects. Structured interviews with mothers were conducted and anthropometric measurements were obtained for 820 mother-child pairs, the follow-up rate after 6 months was 82 per cent. The data were analysed by multivariate regression. Some degree of undernutrition was seen in 83.5 per cent of children and 72.4 per cent of mothers in the sample, moreover the prevalence of undernutrition increased among children at follow-up. Domestic violence was experienced by 34 per cent of mothers in the sample. In multivariate analysis, biological variables explained most of the variance in nutritional status and child growth, followed by health-care seeking and women?s empowerment variables; socio-economic variables explained the least variance. Women?s empowerment variables were significantly associated with child nutrition on enrolment and child growth at follow-up. At follow-up, mother?s prior lifetime experience of physical violence significantly undermined child growth in terms of weight-for-age, and older age at marriage and high mobility of mothers predicted less stunting in their children. In addition to the known investments needed to reduce undernutrition, improving women?s nutrition, promoting gender equality, empowering women, and ending violence against women could further reduce the prevalence of undernutrition in this segment of the Indian population.child nutrition, child growth, domestic violence, nutritional status, women?s empowerment, maternal nutritional status

Large deviations for a class of nonhomogeneous Markov chains

Large deviation results are given for a class of perturbed nonhomogeneous Markov chains on finite state space which formally includes some stochastic optimization algorithms. Specifically, let {P_n} be a sequence of transition matrices on a finite state space which converge to a limit transition matrix P. Let {X_n} be the associated nonhomogeneous Markov chain where P_n controls movement from time n-1 to n. The main statements are a large deviation principle and bounds for additive functionals of the nonhomogeneous process under some regularity conditions. In particular, when P is reducible, three regimes that depend on the decay of certain ``connection'' P_n probabilities are identified. Roughly, if the decay is too slow, too fast or in an intermediate range, the large deviation behavior is trivial, the same as the time-homogeneous chain run with P or nontrivial and involving the decay rates. Examples of anomalous behaviors are also given when the approach P_n\to P is irregular. Results in the intermediate regime apply to geometrically fast running optimizations, and to some issues in glassy physics.Comment: Published at http://dx.doi.org/10.1214/105051604000000990 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org