Relations de récurrence à coefficients aléatoires et lois stables

We consider a multivariate affine stochastic recursion and the corresponding Birkhoff sum along a trajectory. Under a condition on the law of coefficients which is generic, we show that the above sum, suitably normalized, converges in distribution to a stable law, depending essentially on the multiplicative part of the relation. The proof is based on the spectral properties of the associated Markov operator, and on the homogeneity at infinity of the stationary measure.     

Interpretation of the specific heat at the Jahn-Teller phase transition in DyVO4 using a “compressible” Ising model

The specific heat at the Jahn-Teller phase transition in DyVO₄ is too sharply peaked to be explained by simple mean-field theory, but is very well described by using a mean-field model in which the effective interaction increases upon ordering according to J′=J₀′(1+ζ〈σ^z〉²) where ζ is an adjustable parameter.     

The Frobenius complexity of Hibi rings

We study the Frobenius complexity of Hibi rings over fields of characteristic $p>0$. In particular, for a certain class of Hibi rings (which we call ${\omega }^{(?1)}$-level), we compute the limit of the Frobenius complexity as $p\to \infty$.     

Low temperature photoluminescence of GaxIn1−xAs/GaAs strained layer superlattices

The low temperature photoluminescence spectra of several Ga_xIn_1−xAs/GaAs strained layer superlattices have been measured. Excitomic recombination between electrons and holes confined in the ternary layers and conduction band-acceptor transitions have been observed. The excitonic transition energies calculated with a simple model which takes into account both strain and quantization are in good agreement with the measured values provided the additional strain due to the mismatch between the SLS and the buffer layer is taken into account. The hydrogenic acceptor binding energy is smaller in the SLS than in the bulk ternary because the reduction due to the decrease of the hole mass under strain appears to be more important than the two dimensional quantization enhancement in the present samples.     

A hydrogen-nitrogen gas coulometer

The hydrogen-oxygen gas coulometer yields a negative error at small current densities. A hydrogen-nitrogen gas coulometer, employing a hydrazine sulphate electrolyte, and free from this error, is described. A new form of the gas coulometer, employing the hydrazine sulphate electrolyte and suitable for the accurate integration of small quantities of electricity (5 to 20 coulombs) has been developed.