4 citations · 6 across the 6 of their papers we have counts for
13 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…