Sublinear growth of the corrector in stochastic homogenization: Optimal stochastic estimates for slowly decaying correlations

We establish sublinear growth of correctors in the context of stochastic homogenization of linear elliptic PDEs. In case of weak decorrelation and "essentially Gaussian" coefficient fields, we obtain optimal (stretched exponential) stochastic moments for the minimal radius above which the corrector is sublinear. Our estimates also capture the quantitative sublinearity of the corrector (caused by the quantitative decorrelation on larger scales) correctly. The result is based on estimates on the Malliavin derivative for certain functionals which are basically averages of the gradient of the corrector, on concentration of measure, and on a mean value property for $a$-harmonic functions

The \mu-Calculus Alternation Hierarchy Collapses over Structures with Restricted Connectivity

It is known that the alternation hierarchy of least and greatest fixpoint operators in the mu-calculus is strict. However, the strictness of the alternation hierarchy does not necessarily carry over when considering restricted classes of structures. A prominent instance is the class of infinite words over which the alternation-free fragment is already as expressive as the full mu-calculus. Our current understanding of when and why the mu-calculus alternation hierarchy is not strict is limited. This paper makes progress in answering these questions by showing that the alternation hierarchy of the mu-calculus collapses to the alternation-free fragment over some classes of structures, including infinite nested words and finite graphs with feedback vertex sets of a bounded size. Common to these classes is that the connectivity between the components in a structure from such a class is restricted in the sense that the removal of certain vertices from the structure's graph decomposes it into graphs in which all paths are of finite length. Our collapse results are obtained in an automata-theoretic setting. They subsume, generalize, and strengthen several prior results on the expressivity of the mu-calculus over restricted classes of structures.Comment: In Proceedings GandALF 2012, arXiv:1210.202

Physical Characteristics of the Spectral States of Galactic Black Holes

Using simple analytical estimates we show how the physical parameters characterizing different spectral states of the galactic black hole candidates can be determined using spectral data presently available.Comment: 5 pages, 3 figures, to appear in the Proceedings of 4th Compton Symposium, April 27-30, 1997, Williamsburg, Virginia, US

Dynamical clustering and phase separation in suspensions of self-propelled colloidal particles

We study experimentally and numerically a (quasi) two dimensional colloidal suspension of self-propelled spherical particles. The particles are carbon-coated Janus particles, which are propelled due to diffusiophoresis in a near-critical water-lutidine mixture. At low densities, we find that the driving stabilizes small clusters. At higher densities, the suspension undergoes a phase separation into large clusters and a dilute gas phase. The same qualitative behavior is observed in simulations of a minimal model for repulsive self-propelled particles lacking any alignment interactions. The observed behavior is rationalized in terms of a dynamical instability due to the self-trapping of self-propelled particles.Comment: 8 pages including supplemental information, to appear in Phys. Rev. Let

Does geography matter? an empirical investigation into neighbourhood, peer effects and electricity consumption

This thesis consists of four distinct projects which sit at the crossroad between Labour, Education and Environmental Economics. The underlying and unifying theme is the examination of social and geographical inequalities using applied econometrics. In the first project, I estimate the effect of moving into a deprived high-density social housing neighbourhood on the educational attainments of teenagers in England. I exploit the timing of moving, which can be taken as exogenous because of long waiting lists for social housing in high-demand areas, to avoid the usual sorting problems. Using this strategy, I find no evidence for negative effects. The second project investigates the effect of neighbours' characteristics and prior achievements on teenagers' educational outcomes. The study relies on mover-induced variation in neighbourhood quality, whilst controlling for general gentrification trends and other unobservables. The results provide little evidence for significant effects on pupil test score progression. The third project looks at the size, significance and heterogeneity of ability peer effects in secondary schools in England. The methodological innovation is to identify ability peer effects using within-pupil-across-subject variation in students' test scores and peer prior achievements. The chapter shows that it is the low- and high-achievers, who account for most or all of the effect of average peer quality on the educational outcomes of other pupils and that this effect varies across genders. The final project presents -to the best of my knowledge- the first nationwide empirical assessment of residential electricity use in response to the timing of daylight for the US. Employing Geographical Information Systems (GIS), I calculate the solar times of sunrise and sunset for all locations in mainland US and show that two distinct sources of geographical variation can be used to estimate county-level responses in residential electricity consumption. Using both approaches I find that early sunrise is associated with lower residential electricity use in the North, but higher consumption in the South. This is a novel finding with potentially significant policy implications and I offer some suggestions about how future research should examine the behavioural channels that could cause these results