Quenched large deviations for diffusions in a random Gaussian shear flow drift

We prove a full large deviations principle in large time, for a diffusion process with random drift V, which is a centered Gaussian shear flow random field. The large deviations principle is established in a ``quenched'' setting, i.e. is valid almost surely in the randomness of V.Comment: 29 page

Large deviations for Brownian motion in a random scenery

We prove large deviations principles in large time, for the Brownian occupation time in random scenery. The random scenery is constant on unit cubes, and consist of i.i.d. bounded variables, independent of the Brownian motion. This model is a time-continuous version of Kesten and Spitzer's random walk in random scenery. We prove large deviations principles in ``quenched'' and ``annealed'' settings.Comment: 29 page

Random Forests and Networks Analysis

D. Wilson~\cite{[Wi]} in the 1990's described a simple and efficient algorithm based on loop-erased random walks to sample uniform spanning trees and more generally weighted trees or forests spanning a given graph. This algorithm provides a powerful tool in analyzing structures on networks and along this line of thinking, in recent works~\cite{AG1,AG2,ACGM1,ACGM2} we focused on applications of spanning rooted forests on finite graphs. The resulting main conclusions are reviewed in this paper by collecting related theorems, algorithms, heuristics and numerical experiments. A first foundational part on determinantal structures and efficient sampling procedures is followed by four main applications: 1) a random-walk-based notion of well-distributed points in a graph 2) how to describe metastable dynamics in finite settings by means of Markov intertwining dualities 3) coarse graining schemes for networks and associated processes 4) wavelets-like pyramidal algorithms for graph signals.Comment: Survey pape

Algebraic structure of stochastic expansions and efficient simulation

We investigate the algebraic structure underlying the stochastic Taylor solution expansion for stochastic differential systems.Our motivation is to construct efficient integrators. These are approximations that generate strong numerical integration schemes that are more accurate than the corresponding stochastic Taylor approximation, independent of the governing vector fields and to all orders. The sinhlog integrator introduced by Malham & Wiese (2009) is one example. Herein we: show that the natural context to study stochastic integrators and their properties is the convolution shuffle algebra of endomorphisms; establish a new whole class of efficient integrators; and then prove that, within this class, the sinhlog integrator generates the optimal efficient stochastic integrator at all orders.Comment: 19 page

Neutrino oscillation physics with a higher γ\gamma β\beta-beam

The precision measurement and discovery potential of a neutrino factory based on a storage ring of boosted radioactive ions ($\beta$-beam) is re-examined. In contrast with past designs, which assume ion $\gamma$ factors of $\sim 100$ and baselines of L=130 km, we emphasize the advantages of boosting the ions to higher $\gamma$ and increasing the baseline proportionally. In particular, we consider a medium-$\gamma$ scenario ($\gamma \sim 500$, L=730 km) and a high-$\gamma$ scenario ($\gamma \sim 2000$, L = 3000 km).The increase in statistics, which grow linearly with the average beam energy, the ability to exploit the energy dependence of the signal and the sizable matter effects at this longer baseline all increase the discovery potential of such a machine very significantly.Comment: An error corrected, conclusions unchanged. Revised version to appear in Nuclear Physics

Estudio sobre el sistema de almacenamiento de agua caliente sanitaria en un sistema solar térmico

L’objecte d’aquest projecte és el disseny d’una instal·lació solar tèrmica per al subministrament d’Aigua Calenta Sanitària (ACS) a un edifici de 24 habitatges situat a la ciutat de Lleida. La instal·lació constarà d’un sistema d’acumulació tèrmica innovador utilitzant materials de canvi de fase (PCM) i de la posterior experimentació i estudi de la millora de la transferència de calor del PCM a l’aigua mitjançant aletes.El objetivo de este proyecto es el diseño de una instalación solar térmica para el suministro de Agua Caliente Sanitaria (ACS) a un edificio de 24 viviendas situado en la ciudad de Lleida. La instalación constará de un sistema de acumulación térmica innovador utilizando materiales de cambio de fase (PCM) y de la posterior experimentación y estudio de la mejora de la transferencia de calor del PCM a el agua mediante aleta