Thesis (M. Phil.)--University of Hong Kong, 1998. / Includes bibliographical references (leaf 118-122).

Thesis (Ph. D.)--Oregon State University, 1996. / Typescript (photocopy). Includes bibliographical references (leaves 64-67). Also available on the World Wide Web.

Thesis (M.S.)--George Mason University, 2009. / Vita: p. 91. Thesis director: Jens-Peter Kaps. Submitted in partial fulfillment of the requirements for the degree of Master of Science in Computer Engineering. Title from PDF t.p. (viewed Oct. 12, 2009). Includes bibliographical references (p. 88-90). Also issued in print.

Thesis (M.C.S.)--Carleton University, 1992. / Also available in electronic format on the Internet.

Thesis--Wisconsin. / Vita. Includes bibliographical references (leaf 81).

Thesis (Ph. D.)--University of Washington, 1987. / Vita. Bibliography: leaves [213]-215.

The properties of two novel random fibre lasers, in which stimulated Brillouin scattering supplies the effective gain mechanism and Rayleigh scattering along the standard telecommunication optical fibre provides random distributed feedback, are characterised. Firstly, ultra-narrow microwave signals with a Dirac delta function profile are successfully created by beating two random-lasing near-Gaussian beams, arising from the synchronization of optical modes from two Stokes signals with random phase accumulated over the ultra-long optical fibre. This finding provides a completely new approach to synthesise high spectral purity microwave signals from Brillouin fibre lasers with randomised feedback. In addition, we also develop a theoretical model of the random fibre Fabry-Pérot resonator based on the fact that the pump depletion effect naturally selects out the effective Rayleigh feedback regions localised in both ends of this long fibre. A narrow random-laser output with the linewidth of ~860 Hz is experimentally demonstrated and is employed to characterise the linewidth of the pump light. Furthermore, the random laser dynamics is studied and one application towards the physical entropy source is eventually achieved.

No description available.

This thesis examines random variables of one dimension.

Cette thèse a pour objet d’étude divers modèles de marches aléatoires sur les arbres aléatoires.Nous nous sommes consacrés principalement aux aspects qui relevaient à la fois de la théorie des probabilités et de la théorie ergodique. Notre premier modèle est celui des marches aléatoires sur les arbres à longueurs récursives(qui généralise un modèle apparaissant dans un travail récent de Curien et Le Gall). Nous montrons pour ce modèle sous des conditions très générales qu’un phénomène appelé « chute de dimension » se produit pour la mesure harmonique et donnons une formule assez explicite permettant de calculer cette dimension.En utilisant les outils développés pour ce dernier modèle, nous nous intéressons à la marche aléatoire lambda-biaisée sur un arbre de Galton-Watson infini, pour lequel de nombreuses conjectures sont toujours ouvertes. Notre approche nous permet de calculer la dimension de la mesure harmonique en fonction de la loi de la conductance de l’arbre. C’est un résultat nouveau qui nous permet de vérifier numériquement certaines de ces conjectures ouvertes.Le reste de la thèse porte sur un modèle très riche appelé marche aléatoire sur un arbre pondéré aléatoire. D’abord dans le cas transient, où nous montrons par une approche différente de celle des parties précédentes que le phénomène de chute de dimension se produit. Puis sur un cas récurrent appelé sous-diffusif, où nous nous intéressons à la vitesse de convergence vers 0 de la conductance entre la racine et le niveau n de l’arbre lorsque n tend vers l’infini. Nous montrons que la loi limite de cette conductance renormalisée par son espérance est la limite de la martingale de Mandelbrot. / The subject of this thesis is the study of various models of random walks on random trees, with an emphasis on the aspects that fall at the intersection of probability theory and ergodic theory. We called our first model “random walks on Galton-Watson trees with recursive lengths”.It generalizes a model appearing in a recent work by Curien and Le Gall. We show that under fairly general assumptions, a phenomenon called “dimension drop” holds for this model and we give a formula for this dimension. Using the tools developed for the study of the previous model, we turn to the case oft ransient lambda-biased random walks on infinite Galton-Watson trees, for which many famous problems are still open. Our approach allows us to compute the dimension of the harmonic measure as a function of the law of the conductance of the tree. With this new result, we check numerically the validity of some twenty-year-old conjectures.The remainder of this thesis is about a very rich model called random walk on a random weighted Galton-Watson tree. First, we study the transient case, where we show with a different method than in the previous parts, that the dimension drop phenomen on occurs. Then we turn to a recurrent case called subdiffusive and we investigate the rate of decay of the conductance between the root and the n-th level of the tree, as n goes to infinity. We prove that this conductance, suitably renormalized converges to the limit of the Mandelbrot martingale.