Merging for inhomogeneous finite Markov chains, part II: Nash and log-Sobolev inequalities

We study time-inhomogeneous Markov chains with finite state spaces using Nash and logarithmic-Sobolev inequalities, and the notion of $c$-stability. We develop the basic theory of such functional inequalities in the time-inhomogeneous context and provide illustrating examples.Comment: Published in at http://dx.doi.org/10.1214/10-AOP572 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Time inhomogeneous Markov chains with wave-like behavior

Starting from a given Markov kernel on a finite set $V$ and a bijection $g$ of $V$, we construct and study a time inhomogeneous Markov chain whose kernel at time $n$ is obtained from $K$ by transport of $g^{n-1}$. We show that this construction leads to interesting examples, and we obtain quantitative results for some of these examples.Comment: Published in at http://dx.doi.org/10.1214/09-AAP661 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Barry Smith an sich

Festschrift in Honor of Barry Smith on the occasion of his 65th Birthday. Published as issue 4:4 of the journal Cosmos + Taxis: Studies in Emergent Order and Organization. Includes contributions by Wolfgang Grassl, Nicola Guarino, John T. Kearns, Rudolf Lüthe, Luc Schneider, Peter Simons, Wojciech Żełaniec, and Jan Woleński

The mid-infrared extinction law in the darkest cores of the Pipe Nebula

Context. The properties of dust grains, in particular their size distribution, are expected to differ from the interstellar medium to the high-density regions within molecular clouds. Aims. We measure the mid-infrared extinction law produced by dense material in molecular cloud cores. Since the extinction at these wavelengths is caused by dust, the extinction law in cores should depart from that found in low-density environments if the dust grains have different properties. Methods. We use the unbiased LINES method to measure the slope of the reddening vectors in color-color diagrams. We derive the mid-infrared extinction law toward the dense cores B59 and FeSt 1-457 in the Pipe Nebula over a range of visual extinction between 10 and 50 magnitudes, using a combination of Spitzer/IRAC, and ESO NTT/VLT data. Results. The mid-infrared extinction law in both cores departs significantly from a power-law between 3.6 and 8 micron, suggesting that these cores contain dust with a considerable fraction of large dust grains. We find no evidence for a dependence of the extinction law with column density up to 50 magnitudes of visual extinction in these cores, and no evidence for a variation between our result and those for other clouds at lower column densities reported elsewhere in the literature. This suggests that either large grains are present even in low column density regions, or that the existing dust models need to be revised at mid-infrared wavelengths. We find a small but significant difference in the extinction law of the two cores, that we tentatively associate with the onset of star formation in B59.Comment: 8 pages, 6 figures. Accepted to A&

Critical Properties of the Superfluid - Bose Glass Transition in Two Dimensions

We investigate the superfluid (SF) to Bose glass (BG) quantum phase transition using extensive quantum Monte Carlo simulations of two-dimensional hard-core bosons in a random box potential. $T=0$ critical properties are studied by thorough finite-size scaling of condensate and SF densities, both vanishing at the same critical disorder $W_c=4.80(5)$. Our results give the following estimates for the critical exponents: $z=1.85(15)$, $\nu=1.20(12)$, $\eta=-0.40(15)$. Furthermore, the probability distribution of the SF response $P(\ln\rho_{\rm sf})$ displays striking differences across the transition: while it narrows with increasing system sizes $L$ in the SF phase, it broadens in the BG regime, indicating an absence of self-averaging, and at the critical point $P(\ln\rho_{\rm sf}+z \ln L)$ is scale invariant. Finally, high-precision measurements of the local density rule out a percolation picture for the SF-BG transition.Comment: 4 pages, 5 figures + supplementary materia

From Strong to Weak Coupling Regime in a Single GaN Microwire up to Room Temperature

Large bandgap semiconductor microwires constitute a very advantageous alternative to planar microcavities in the context of room temperature strong coupling regime between exciton and light. In this work we demonstrate that in a GaN microwire, the strong coupling regime is achieved up to room temperature with a large Rabi splitting of 125 meV never achieved before in a Nitride-based photonic nanostructure. The demonstration relies on a method which doesn't require any knowledge \'a priori on the photonic eigenmodes energy in the microwire, i.e. the details of the microwire cross-section shape. Moreover, using a heavily doped segment within the same microwire, we confirm experimentally that free excitons provide the oscillator strength for this strong coupling regime. The measured Rabi splitting to linewidth ratio of 15 matches state of the art planar Nitride-based microcavities, in spite of a much simpler design and a less demanding fabrication process. These results show that GaN microwires constitute a simpler and promising system to achieve electrically pumped lasing in the strong coupling regime.Comment: 14 pages, 4 figure