Poisson boundary of a relativistic diffusion in curved space-times: an example

We study in details the long-time asymptotic behavior of a relativistic diffusion taking values in the unitary tangent bundle of a curved Lorentzian manifold, namely a spatially flat and fast expanding Robertson-Walker space-time. We prove in particular that the Poisson boundary of the diffusion can be identified with the causal boundary of the underlying manifold.Comment: 16 pages, 2 figure

Asymptotic behavior of a relativistic diffusion in Robertson-Walker space-times

We determine the long-time asymptotic behavior of a relativistic diffusion taking values in the unitary tangent bundle of a Robertson-Walker space-time. We prove in particular that when approaching the explosion time of the diffusion, its projection on the base manifold almost surely converges to a random point of the causal boundary and we also describe the behavior of the tangent vector in the neighborhood of this limiting point.Comment: 42 pages, 6 figure

Growth of layered Lu2_2Fe3_3O7_7 and Lu3_3Fe4_4O10_{10} single crystals exhibiting long-range charge order via the optical floating-zone method

We report the controlled growth of single crystals of intercalated layered Lu$_{1+n}$Fe$_{2+n}$O$_{4+3n-\delta}$ ($n$=1,2) with different oxygen stoichiometries ${\delta}$. For the first time crystals sufficiently stoichiometric to exhibit superstructure reflections in X-ray diffraction attributable to charge ordering were obtained. The estimated correlation lengths tend to be smaller than for not intercalated LuFe$_2$O$_4$. For Lu$_2$Fe$_3$O$_7$, two different superstructures were observed, one an incommensurate zigzag pattern similar to previous observations by electron diffraction, the other an apparently commensurate pattern with ($\frac{1}{3}\frac{1}{3}0$) propagation. Implications for the possible charge order in the bilayers are discussed. Magnetization measurements suggest reduced magnetic correlations and the absence of an antiferromagnetic phase.Comment: 7pages, 7figure

Universality of the mean number of real zeros of random trigonometric polynomials under a weak Cramer condition

We investigate the mean number of real zeros over an interval $[a,b]$ of a random trigonometric polynomial of the form $\sum_{k=1}^n a_k \cos(kt)+b_k \sin(kt)$ where the coefficients are i.i.d. random variables. Under mild assumptions on the law of the entries, we prove that this mean number is asymptotically equivalent to $\frac{n(b-a)}{\pi\sqrt{3}}$ as $n$ goes to infinity, as in the known case of standard Gaussian coefficients. Our principal requirement is a new Cramer type condition on the characteristic function of the entries which does not only hold for all continuous distributions but also for discrete ones in a generic sense. To our knowledge, this constitutes the first universality result concerning the mean number of zeros of random trigonometric polynomials. Besides, this is also the first time that one makes use of the celebrated Kac-Rice formula not only for continuous random variables as it was the case so far, but also for discrete ones. Beyond the proof of a non asymptotic version of Kac-Rice formula, our strategy consists in using suitable small ball estimates and Edgeworth expansions for the Kolmogorov metric under our new weak Cramer condition, which both constitute important byproducts of our approach

Trends to equilibrium for a class of relativistic diffusions

We address the question of the trends to equilibrium for a large class C of relativistic diffusions. We show the existence of a spectral gap using the Lyapounov method and deduce the exponential decay of the distance to equilibrium in L2-norm and in total variation. A similar result was obtained recently in arXiv:1009.5086 for a particular process of the class C.Comment: 10 page

Anisotropic properties of MgB2 by torque magnetometry

Anisotropic properties of superconducting MgB2 obtained by torque magnetometry are compared to theoretical predictions, concentrating on two issues. Firstly, the angular dependence of Hc2 is shown to deviate close to Tc from the dependence assumed by anisotropic Ginzburg-Landau theory. Secondly, from the evaluation of torque vs angle curves it is concluded that the anisotropy of the penetration depth gamma_lambda has to be substantially higher at low temperature than theoretical estimates, at least in fields higher than 0.2 T.Comment: 2 p.,2 Fig., submitted to Physica C (M2S-Rio proceedings); v2: 1 ref adde

Central Limit Theorem for a Class of Relativistic Diffusions

Two similar Minkowskian diffusions have been considered, on one hand by Barbachoux, Debbasch, Malik and Rivet ([BDR1], [BDR2], [BDR3], [DMR], [DR]), and on the other hand by Dunkel and H\"anggi ([DH1], [DH2]). We address here two questions, asked in [DR] and in ([DH1], [DH2]) respectively, about the asymptotic behaviour of such diffusions. More generally, we establish a central limit theorem for a class of Minkowskian diffusions, to which the two above ones belong. As a consequence, we correct a partially wrong guess in [DH1].Comment: 20 page