Threshold for monotone symmetric properties through a logarithmic Sobolev inequality

Threshold phenomena are investigated using a general approach, following Talagrand [Ann. Probab. 22 (1994) 1576--1587] and Friedgut and Kalai [Proc. Amer. Math. Soc. 12 (1999) 1017--1054]. The general upper bound for the threshold width of symmetric monotone properties is improved. This follows from a new lower bound on the maximal influence of a variable on a Boolean function. The method of proof is based on a well-known logarithmic Sobolev inequality on $\{0,1\}^n$. This new bound is shown to be asymptotically optimal.Comment: Published at http://dx.doi.org/10.1214/009117906000000287 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Noise-stability and central limit theorems for effective resistance of random electric networks

We investigate the (generalized) Walsh decomposition of point-to-point effective resistances on countable random electric networks with i.i.d. resistances. We show that it is concentrated on low levels, and thus point-to-point effective resistances are uniformly stable to noise. For graphs that satisfy some homogeneity property, we show in addition that it is concentrated on sets of small diameter. As a consequence, we compute the right order of the variance and prove a central limit theorem for the effective resistance through the discrete torus of side length $n$ in $\mathbb {Z}^d$, when $n$ goes to infinity.Comment: Published at http://dx.doi.org/10.1214/14-AOP996 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Is inequality harmful for the environment in a growing economy ?

In this paper we investigate the relationship between inequality and the environment in a growing economy from a political economy perspective. We consider an endogenous growth economy, where growth generates pollution and a deterioration of the environment. Public expenditures may either be devoted to supporting growth or abating pollution. The decision over the public programs is done in a direct democracy, with simple majority rule. We prove that the median voter is decisive and show that inequality is harmful for the environment : the poorer the median voter relative to the average individual, the less she will tax and devote resources to the environment, preferring to support growth.Inequality, growth, environmental policy, political economy.

Sharp threshold for percolation on expanders

We study the appearance of the giant component in random subgraphs of a given large finite graph G=(V,E) in which each edge is present independently with probability p. We show that if G is an expander with vertices of bounded degree, then for any c in ]0,1[, the property that the random subgraph contains a giant component of size c|V| has a sharp threshold.Comment: Published in at http://dx.doi.org/10.1214/10-AOP610 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Chemical Vapor Deposition of silicon nanodots on TiO2 submicronic powders in vibrated fluidized bed

Silicon nanodots have been deposited on TiO2 submicronic powders in a vibrated Fluidized Bed Chemical Vapor Deposition (FBCVD) reactor from silane SiH4. Deposition conditions involving very low deposition rates have been studied. After treatment, powders are under the form of micronic agglomerates. In the operating range tested, this agglomerates formation mainly depends on the fluidization conditions and not on the CVD parameters. The best results have been obtained for anatase TiO2 powders for which the conditions of fluidization have been the most optimized. For these anatase powders, agglomerates are porous. SEM and TEM imaging prove that silicon nanodots (8-10 nm in size) have been deposited on the surface of particles and that this deposition is uniform on the whole powders and conformal around each grain, even if not fully continuous. Raman spectroscopy shows that the TiO2 powders have been partially reduced into TiO2-x during deposition. The TiO2 stoichiometry can be recovered by annealing under air, and IR spectroscopy indicates that the deposited silicon nanodots have been at least partly oxidized into SiO2 after this annealing