arXiv subjects

Patricia Alonso Ruiz

Publications and source records attributed to Patricia Alonso Ruiz.

22 records · Page 2Linked to original sources

arXiv2016

Entropy-based inhomogeneity detection in porous media

We study a change-point problem for random fields based on a univariate detection of outliers via the $3σ$-rule in order to recognize inhomogeneities in porous media. In particular, we focus on fibre reinforced polymers modeled by stochastic fibre processes with high fibre intensity and search for abrupt changes in the direction of the fibres. As a measure of change, the entropy of the directional distribution is locally estimated within a window that scans the region to be analyzed.

stat.ME↗

arXiv2016

The limit theorem for maximum of partial sums of exchangeable random variables

We obtain the analogue of the classical result by Erdös and Kac on the limiting distribution of the maximum of partial sums for exchangeable random variables with zero mean and variance one. We show that, if the conditions of the central limit theorem of Blum et al. hold, the limit coincides with the classical one. Under more general assumptions, the probability of the random variables having conditional negative drift appears in the limiting distribution.

math.PR↗

arXiv2015

Energy and Laplacian on Hanoi-type fractal quantum graphs

This article studies potential theory and spectral analysis on compact metric spaces, which we refer to as fractal quantum graphs. These spaces can be represented as a (possibly infinite) union of 1-dimensional intervals and a totally disconnected (possibly uncountable) compact set, which roughly speaking represents the set of junction points. Classical quantum graphs and fractal spaces such as the Hanoi attractor are included among them. We begin with proving the existence of a resistance form on the Hanoi attractor, and go on to establish heat kernel estimates and upper and lower bounds on the eigenvalue counting function of Laplacians corresponding to weakly self-similar measures on the Hanoi attractor. These estimates and bounds rely heavily on the relation between the length and volume scaling factors of the fractal. We then state and prove a necessary and sufficient condition for the existence of a resistance form on a general fractal quantum graph. Finally, we extend our spectral results to a large class of weakly self-similar fractal quantum graphs.

math-ph↗

arXiv2014

Weyl asymptotics for Hanoi attractors

The asymptotic behaviour of the eigenvalue counting function of Laplacians on Hanoi attractors is determined. To this end, Dirichlet and resistance forms are constructed. Due to the non self-similarity of these sets, the classical construction of the Laplacian for p.c.f. self-similar fractals has to be modified by combining discrete and quantum graphs methods.

math.SP↗