13 citations · 27 across the 12 of their papers we have counts for
15 papers
Dirac measures can be quantum limits on the Sierpinski gasket
Patricia Alonso Ruiz, Nikolay Tzvetkov
We prove that on the Sierpinski gasket, a prototype of compact fractal space, Dirac distributions arise as the weak limit of probability measures associated with sequences of high…
Towards Liouville Quantum Gravity on fractals
Patricia Alonso Ruiz, Eva Kopfer
Motivated by the recent construction of fractional Gaussian fields on the Sierpinski gasket, we study those Gaussian fields whose covariance function exhibits a logarithmic behavio…
Oscillations of BV measures on nested fractals
Patricia Alonso Ruiz, Fabrice Baudoin
Motivated by recent developments in the theory of bounded variation functions on nested fractals, this paper studies the exact asymptotics of functionals related to the total varia…
Minimal gap in the spectrum of the Sierpinski gasket
Patricia Alonso Ruiz
This paper studies the size of the minimal gap between any two consecutive eigenvalues in the Dirichlet and in the Neumann spectrum of the standard Laplace operator on the Sierpins…
Yet another heat semigroup characterization of BV functions on Riemannian manifolds
Patricia Alonso Ruiz, Fabrice Baudoin
This paper provides a characterization of functions of bounded variation (BV) in a compact Riemannian manifold in terms of the short time behavior of the heat semigroup. In particu…
Gagliardo-Nirenberg, Trudinger-Moser and Morrey inequalities on Dirichlet spaces
Patricia Alonso Ruiz, Fabrice Baudoin
With a view towards Riemannian or sub-Riemannian manifolds, RCD metric spaces and specially fractals, this paper makes a step further in the development of a theory of heat semigro…
BV functions and fractional Laplacians on Dirichlet spaces
Patricia Alonso Ruiz, Fabrice Baudoin, Li Chen +3
We study Besov critical exponents and isoperimetric and Sobolev inequalities associated with fractional Laplacians on metric measure spaces. The main tool is the theory of he…
Heat kernel analysis on diamond fractals
Patricia Alonso Ruiz
This paper presents a detailed analysis of the heat kernel on an -parameter family of compact metric measure spaces, which do not satisfy the volume d…
Besov class via heat semigroup on Dirichlet spaces I: Sobolev type inequalities
Patricia Alonso-Ruiz, Fabrice Baudoin, Li Chen +3
We introduce heat semigroup-based Besov classes in the general framework of Dirichlet spaces. General properties of those classes are studied and quantitative regularization estima…
Analysis on hybrid fractals
Patricia Alonso Ruiz, Yuming Chen, Haotian Gu +2
We introduce hybrid fractals as a class of fractals constructed by gluing several fractal pieces in a specific manner and study energy forms and Laplacians on them. We consider in…
Power dissipation in fractal Feynman-Sierpinski AC circuits
Patricia Alonso Ruiz
This paper studies the concept of power dissipation in infinite graphs and fractals associated with passive linear networks consisting of non-dissipative elements. In particular, w…
Entropy-based inhomogeneity detection in porous media
Patricia Alonso Ruiz, Evgeny Spodarev
We study a change-point problem for random fields based on a univariate detection of outliers via the -rule in order to recognize inhomogeneities in porous media. In particular…
Completely Symmetric Resistance Forms on the Stretched Sierpinski Gasket
Patricia Alonso Ruiz, Uta Freiberg, Jun Kigami
The stretched Sierpinski gasket, SSG for short, is the space obtained by replacing every branching point of the Sierpinski gasket by an interval. It has also been called "deformed…
The limit theorem for maximum of partial sums of exchangeable random variables
Patricia Alonso Ruiz, Alexander S. Rakitko
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 var…
Weyl asymptotics for Hanoi attractors
Patricia Alonso Ruiz, Uta Freiberg
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 th…