Estimation in a growth study with irregular measurement times

Between 1982 and 1988 a growth study was carried out at the Division of Pediatric Oncology of the University Hospital of Groningen. A special feature of the project was that sample sizes are small and that ages at entry may be very different. In addition the intended design was not fully complied with. This paper highlights some aspects of the statistical analysis which is based on (1) reference scores, (2) statistical procedures allowing for an irregular pattern of measurement times caused by missing data and shifted measurement times

A Brownian particle in a microscopic periodic potential

We study a model for a massive test particle in a microscopic periodic potential and interacting with a reservoir of light particles. In the regime considered, the fluctuations in the test particle's momentum resulting from collisions typically outweigh the shifts in momentum generated by the periodic force, and so the force is effectively a perturbative contribution. The mathematical starting point is an idealized reduced dynamics for the test particle given by a linear Boltzmann equation. In the limit that the mass ratio of a single reservoir particle to the test particle tends to zero, we show that there is convergence to the Ornstein-Uhlenbeck process under the standard normalizations for the test particle variables. Our analysis is primarily directed towards bounding the perturbative effect of the periodic potential on the particle's momentum.Comment: 60 pages. We reorganized the article and made a few simplifications of the conten

Metal-Kondo insulating transitions and transport in one dimension

We study two different metal-insulating transitions possibly occurring in one-dimensional Kondo lattices. First, we show how doping the pure Kondo lattice model in the strong-coupling limit, results in a Pokrovsky-Talapov transition. This produces a conducting state with a charge susceptibility diverging as the inverse of the doping, that seems in agreement with numerical datas. Second, in the weak-coupling region, Kondo insulating transitions arise due to the consequent renormalization of the backward Kondo scattering. Here, the interplay between Kondo effect and electron-electron interactions gives rise to significant phenomena in transport, in the high-temperature delocalized (ballistic) regime. For repulsive interactions, as a perfect signature of Kondo localization, the conductivity is found to decrease monotonically with temperature. When interactions become attractive, spin fluctuations in the electron (Luttinger-type) liquid are suddenly lowered. The latter is less localized by magnetic impurities than for the repulsive counterpart, and as a result a large jump in the Drude weight and a maximum in the conductivity arise in the entrance of the Kondo insulating phase. These can be viewed as remnants of s-wave superconductivity arising for attractive enough interactions. Comparisons with transport in the single impurity model are also performed. We finally discuss the case of randomly distributed magnetic defects, and the applications on persistent currents of mesoscopic rings.Comment: 21 pages, two columns, 5 figures and 1 table; Final version: To appear in Physical Review

Note on Randomized Filtered Experiments in Presence of Nuisance Parameters

Note on randomized filtered experiments in presence of nuisance parameter