64 research outputs found
On Contraction Properties for Products of Markov Driven Random Matrices
We describe contraction properties on pro jective spaces for products of matrices governed by Markov chains which satisfy strong mixing conditions. Assuming that the subgroup generated by the corresponding matrices is "large" we show in particular that the top Lyapunov exponent of their product has multiplicity one and we give an exposition of the related results
On random topological Markov chains with big images and preimages
We introduce a relative notion of the 'big images and preimages'-property for
random topological Markov chains. This then implies that a relative version of
the Ruelle-Perron-Frobenius theorem holds with respect to summable and locally
Hoelder continuous potentials.Comment: Corrected and extended version of the article published in
Stochastics and Dynamics 201
Equilibrium states of the pressure function for products of matrices
Let be a non-trivial family of complex
matrices, in the sense that for any , there exists such that . Let be the pressure function of . We show
that for each , there are at most ergodic -equilibrium states of
, and each of them satisfies certain Gibbs property.Comment: 12 pages. To appear in DCD
Matrix valued Brownian motion and a paper by Polya
We give a geometric description of the motion of eigenvalues of a Brownian
motion with values in some matrix spaces. In the second part we consider a
paper by Polya where he introduced a function close to the Riemann zeta
function, which satisfies Riemann hypothesis. We show that each of these two
functions can be related to Brownian motion on a symmetric space
DISTRIBUTIONAL AND LOCAL LIMIT LAWS FOR A CLASS OF ITERATED MAPS THAT CONTRACT ON AVERAGE
Transiting exoplanets from the CoRoT space mission. VIII. CoRoT-7b: the first super-Earth with measured radius
Copyright © The European Southern Observatory (ESO)Aims. We report the discovery of very shallow (ΔF/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 caused by 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 used CoRoT colours 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 were derived from optical spectra, which were then combined with the CoRoT light curve to derive parameters of the companion.
Results. We examined all conceivable cases of false positives carefully, and all the tests support the planetary hypothesis. Blends with separation >0.40'' or triple systems are almost excluded with a 8 × 10−4 risk left. We conclude that, inasmuch 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.
Conclusions. CoRoT-7b is very likely the first Super-Earth with a measured radius. This object illustrates what will probably become a common situation with missions such as Kepler, namely the need to establish the planetary origin of transits in the absence of a firm radial velocity detection and mass measurement. The composition of CoRoT-7b remains loosely constrained without a precise mass. A very high surface temperature on its irradiated face, ≈1800–2600 K at the substellar point, and a very low one, ≈50 K, on its dark face assuming no atmosphere, have been derived
Une majoration universelle des fonctions de concentration sur les groupes localement compacts non compacts
- …