The Matsumoto and Yor process and infinite dimensional hyperbolic space

The Matsumoto\,--Yor process is $\int\_0^t \exp(2B\_s-B\_t)\, ds$, where $(B\_t)$ is a Brownian motion. It is shown that it is the limit of the radial part of the Brownian motion at the bottom of the spectrum on the hyperbolic space of dimension $q$, when $q$ tends to infinity. Analogous processes on infinite series of non compact symmetric spaces and on regular trees are described.Comment: 3

Pitman transforms and Brownian motion in the interval viewed as an affine alcove

Pitman's theorem states that if {Bt, t $\ge$ 0} is a one-dimensional Brownian motion, then {Bt -- 2 inf s$\le$t Bs, t $\ge$ 0} is a three dimensional Bessel process, i.e. a Brownian motion conditioned in Doob sense to remain forever positive. In this paper one gives a similar representation for the Brownian motion in an interval. Due to the double barrier, it is much more involved and only asymptotic. This uses the fact that the interval is an alcove of the Affine Lie algebra A 1 1

Littelmann paths and brownian paths

We study some path transformations related to Littelmann path model and their applications to representation theory and Brownian motion in a Weyl chamber.Comment: 30 pages, 1 figur

Intrinsic limits governing MBE growth of Ga-assisted GaAs nanowires on Si(111)

Diffusion-enhanced and desorption-limited growth regimes of Ga-assisted GaAs nanowires were identified. In the latter regime, the number of vertical NWs with a narrow length distribution was increased by raising the growth temperature. The maximum axial growth rate; which can be quantified by the supplied rate of As atoms, is achieved when a dynamical equilibrium state is maintained in Ga droplets i.e. the number of impinging As atoms on the droplet surface is equivalent to that of direct deposited Ga atoms combining with the diffusing ones. The contribution of Ga diffusion to the wire growth was evidenced by the diameter-dependent NW axial growth rate

On Eigenvalue spacings for the 1-D Anderson model with singular site distribution

We study eigenvalue spacings and local eigenvalue statistics for 1D lattice Schrodinger operators with Holder regular potential, obtaining a version of Minami's inequality and Poisson statistics for the local eigenvalue spacings. The main additional new input are regular properties of the Furstenberg measures and the density of states obtained in some of the author's earlier work.Comment: 13 page

Overdoped Cuprates With High Temperature Superconducting Transitions

Evidence for High Tc cuprate superconductivity is found in a region of the phase diagram where non-superconducting Fermi liquid metals are expected. Cu valences estimated independently from both x-ray absorption near-edge structure (XANES) and bond valence sum (BVS) measurements are > 2.3 for structures in the homologous series (Cu0.75Mo0.25)Sr2(Y,Ce)sCu2O5+2s+{\delta} with s = 1, 2, 3, and 4. The s = 1 member, (Cu0.75Mo0.25)Sr2YCu2O7+{\delta}, 0 \leq {\delta} \leq 0.5, is structurally related to YBa2Cu3O7 in which 25% of the basal Cu cations [i.e. those in the chain layer] are replaced by Mo, and the Ba cations are replaced by Sr. After oxidation under high pressure the s = 1 member becomes superconducting with Tc = 88K. The Cu valence is estimated to be ~2.5, well beyond the ~2.3 value for which other High-Tc cuprates are considered to be overdoped Fermi liquids. The increase in valence is attributed to the additional 0.5 oxygen ions added per chain upon oxidation. The record short apical oxygen distance, at odds with current theory, suggests the possibility of a new pairing mechanism but further experiments are urgently needed to obtain more direct evidence. From the structural point of view the members with s \geq 2 are considered to be equivalent to single-layer cuprates. All have Tc ~ 56 K which is significantly higher than expected because they also have higher than expected Cu valences. The XANES-determined valences normalized to give values in the CuO2 layers are 2.24, 2.25, and 2.26 for s = 2, 3, and 4, while the BVS values determined for the valence in the CuO2 layer alone are 2.31-2.34 for the s = 2 and 3 members. No evidence for periodic ordering has been detected by electron diffraction and high resolution imaging studies. The possibility that the charge reservoir layers are able to screen long range coulomb interactions and thus enhance Tc is discussed

Transport in the random Kronig-Penney model

The Kronig-Penney model with random Dirac potentials on the lattice \ZM has critical energies at which the Lyapunov exponent vanishes and the density of states has a van Hove singularity. This leads to a non-trivial quantum diffusion even though the spectrum is known to be pure-point

Influence of the Oryza sativa genotype on the fertility and quantitative traits of F1 hybrids between the two cultivated rice species O. sativa L. and O. glaberrima Steud.

Des croisements ont été réalisés entre les deux espèces de riz cultivé, en utilisant un parent #Oryza glaberrima constant et 14 cultivars d'#O. sativa, dont 11 traditionnels africains. Les hybrides F1 ont été étudiés pour leur fertilité et des caractères quantitatifs. L'analyse de ces derniers a montré la position intermédiaire des F1S par rapport aux lignées parentales et l'héritabilité élevée de plusieurs caractères dont la densité de ramifications secondaires sur la panicule. Tous les hybrides F1 ont présenté une fertilité paniculaire nulle, et seule l'observation du pollen a permis de discriminer les différentes combinaisons. Les hybrides issus de deux cultivars d'#O. sativa introgressés par l'espèce sauvage #O. longistaminata se sont montrés particulièrement stériles. (Résumé d'auteur