arXiv subjects

Marcelo Ventura Freire

Publications and source records attributed to Marcelo Ventura Freire.

3 recordsLinked to original sources

arXiv2017

Self-similar resistive circuits as fractal-like structures

In the present work we explore resistive circuits where the individual resistors are arranged in fractal-like patterns. These circuits have some of the characteristics typically found in geometric fractals, namely self-similarity and scale invariance. Considering resistive circuits as graphs, we propose a definition of self-similar circuits which mimics a self-similar fractal. General properties of the resistive circuits generated by this approach are investigated, and interesting examples are commented in detail. Specifically, we consider self-similar resistive series, tree-like resistive networks and Sierpinski's configurations with resistors.

physics.gen-ph↗

arXiv2014

Application of moderate deviation techniques to prove Sinai's Theorem on RWRE

We apply the techniques developed in Comets and Popov (2003) to present a new proof to Sinai's theorem (Sinai, 1982) on one-dimensional random walk in random environment (RWRE), working in a scale-free way to avoid rescaling arguments and splitting the proof in two independent parts: a quenched one, related to the measure $P_ω$ conditioned on a fixed, typical realization $ω$ of the environment, and an annealed one, related to the product measure $\mathbb{P}$ of the environment $ω$. The quenched part still holds even if we use another measure (possibly dependent) for the environment.

math.PR↗

arXiv2006

Percolation for the stable marriage of Poisson and Lebesgue

Let $Ξ$ be the set of points (we call the elements of $Ξ$ centers) of Poisson process in $\R^d$, $d\geq 2$, with unit intensity. Consider the allocation of $\R^d$ to $Ξ$ which is stable in the sense of Gale-Shapley marriage problem and in which each center claims a region of volume $α\leq 1$. We prove that there is no percolation in the set of claimed sites if $α$ is small enough, and that, for high dimensions, there is percolation in the set of claimed sites if $α<1$ is large enough.

math.PR↗