Convergence to stable laws for multidimensional stochastic recursions: the case of regular matrices

Given a sequence $(M_{n},Q_{n})_{n\ge 1}$ of i.i.d.\ random variables with generic copy $(M,Q) \in GL(d, \R) \times \R^d$, we consider the random difference equation (RDE) $$R_{n}=M_{n}R_{n-1}+Q_{n},$$ $n\ge 1$, and assume the existence of $\kappa >0$ such that \lim_{n \to \infty}(\E{\norm{M_1 ... M_n}^\kappa})^{\frac{1}{n}} = 1 . We prove, under suitable assumptions, that the sequence $S_n = R_1 + ... + R_n$, appropriately normalized, converges in law to a multidimensional stable distribution with index $\kappa$. As a by-product, we show that the unique stationary solution $R$ of the RDE is regularly varying with index $\kappa$, and give a precise description of its tail measure. This extends the prior work http://arxiv.org/abs/1009.1728v3 .Comment: 15 page

Transiting exoplanets from the CoRoT space mission VIII. CoRoT-7b: the first Super-Earth with measured radius

We report the discovery of very shallow (DF/F = 3.4 10-4), periodic dips in the light curve of an active V = 11.7 G9V star observed by the CoRoT satellite, which we interpret as due to the presence of a transiting companion. We describe the 3-colour CoRoT data and complementary ground-based observations that support the planetary nature of the companion. Methods. We use CoRoT color information, good angular resolution ground-based photometric observations in- and out- of transit, adaptive optics imaging, near-infrared spectroscopy and preliminary results from Radial Velocity measurements, to test the diluted eclipsing binary scenarios. The parameters of the host star are derived from optical spectra, which were then combined with the CoRoT light curve to derive parameters of the companion. We examine carefully all conceivable cases of false positives, and all tests performed support the planetary hypothesis. Blends with separation larger than 0.40 arcsec or triple systems are almost excluded with a 8 10-4 risk left. We conclude that, as far as we have been exhaustive, we have discovered a planetary companion, named CoRoT-7b, for which we derive a period of 0.853 59 +/- 3 10-5 day and a radius of Rp = 1.68 +/- 0.09 REarth. Analysis of preliminary radial velocity data yields an upper limit of 21 MEarth for the companion mass, supporting the finding. CoRoT-7b is very likely the first Super-Earth with a measured radius.Comment: Accepted in Astronomy and Astrophysics; typos and language corrections; version sent to the printer w few upgrade

Glucagon-like Peptide 1 Conjugated to Recombinant Human Serum Albumin Variants with Modified Neonatal Fc Receptor Binding Properties. Impact on Molecular Structure and Half-Life

Glucagon-like peptide 1 (GLP-1) is a small incretin hormone stimulated by food intake, resulting in an amplification of the insulin response. Though GLP-1 is interesting as a drug candidate for the treatment of type 2 diabetes mellitus, its short plasma half-life of <3 min limits its clinical use. A strategy for extending the half-life of GLP-1 utilizes the long half-life of human serum albumin (HSA) by combining the two via chemical conjugation or genetic fusion. HSA has a plasma half-life of around 21 days because of its interaction with the neonatal Fc receptor (FcRn) expressed in endothelial cells of blood vessels, which rescues circulating HSA from lysosomal degradation. We have conjugated GLP-1 to C34 of native sequence recombinant HSA (rHSA) and two rHSA variants, one with increased and one with decreased binding affinity for human FcRn. We have investigated the impact of conjugation on FcRn binding affinities, GLP-1 potency, and pharmacokinetics, combined with the solution structure of the rHSA variants and GLP-1–albumin conjugates. The solution structures, determined by small-angle X-ray scattering, show the GLP-1 pointing away from the surface of rHSA. Combining the solution structures with the available structural information about the FcRn and GLP-1 receptor obtained from X-ray crystallography, we can explain the observed <i>in vitro</i> and <i>in vivo</i> behavior. We conclude that the conjugation of GLP-1 to rHSA does not affect the interaction between rHSA and FcRn, while the observed decrease in the potency of GLP-1 can be explained by a steric hindrance of binding of GLP-1 to its receptor

Effective-Range Expansion of the Neutron-Deuteron Scattering Studied by a Quark-Model Nonlocal Gaussian Potential

The S-wave effective range parameters of the neutron-deuteron (nd) scattering are derived in the Faddeev formalism, using a nonlocal Gaussian potential based on the quark-model baryon-baryon interaction fss2. The spin-doublet low-energy eigenphase shift is sufficiently attractive to reproduce predictions by the AV18 plus Urbana three-nucleon force, yielding the observed value of the doublet scattering length and the correct differential cross sections below the deuteron breakup threshold. This conclusion is consistent with the previous result for the triton binding energy, which is nearly reproduced by fss2 without reinforcing it with the three-nucleon force.Comment: 21 pages, 6 figures and 6 tables, submitted to Prog. Theor. Phy

Invariant Measure for Quantum Trajectories

International audienceWe study a class of Markov chains that model the evolution of a quantum system subject to repeated measurements. Each Markov chain in this class is defined by a measure on the space of matrices, and is then given by a random product of correlated matrices taken from the support of the defining measure. We give natural conditions on this support that imply that the Markov chain admits a unique invariant probability measure. We moreover prove the geometric convergence towards this invariant measure in the Wasserstein metric. Standard techniques from the theory of products of random matrices cannot be applied under our assumptions, and new techniques are developed, such as maximum likelihood-type estimations

Chemical profile and magnetoresistance of Ga1−x Mnx As/GaAs/AlAs/GaAs/ Ga1−x Mnx As tunnel junctions

International audienc