arXiv subjects

Isabella Alvarenga

Publications and source records attributed to Isabella Alvarenga.

3 recordsLinked to original sources

arXiv2026

Interface for variants of the contact process

We study two one-dimensional variants of the contact process: the contact-and-barrier process, where the population evolves in a region delimited by a randomly moving barrier, and the multitype contact process, in which two species compete for space. The contact-and-barrier process is started with the barrier at the origin and all sites to its right occupied, while the multitype contact process is started from the Heaviside configuration with species 1 to the left of the origin and species 2 to the right. We prove that both models exhibit tight interfaces and that, after centring by an appropriate deterministic speed, the interface position satisfies a central limit theorem. Our analysis relies on a renewal-time method based on a novel construction called patchwork construction, in which the processes are built by concatenating space-time evolutions over successive time intervals of random length, providing a more convenient framework for defining the renewal times that drive the proofs.

math.PR↗

arXiv2026

Sharkovskiis theorem under small random perturbations

We establish a Sharkovskii-type theorem for a class of discrete random dynamical systems via the random Conley index. Using the continuation property of the Conley index, we extend classical forcing results to random systems obtained from small random perturbations of one-dimensional maps. In contrast to earlier measure-theoretic results, which are typically subject to an inherent period-doubling ambiguity (realizing period $n$ or $2n$), our topological approach allows us to detect random periodic points and orbits with precise minimal periods. This yields realisation results for arbitrary finite tails of the Sharkovskii ordering. These results are illustrated by constructing random periodic orbits for perturbed versions of the tent map and the logistic map.

math.DS↗

arXiv2025

The Rightmost Particle of the Contact Process on Dynamic Random Environments

We study the behaviour of the rightmost occupied site in two models: the Spont process and the contact process with inherited sterility, in dimension 1. Both can be viewed as contact processes evolving in dynamic random environments, where the environment may itself depend on the state of the process. In the Spont process, blocking particles appear spontaneously, while in the inherited sterility model, sterile sites arise as offspring of occupied ones. Each model presents distinct mathematical challenges: the Spont process lacks self-duality, whereas the inherited sterility process is non-attractive. We establish a law of large numbers and a central limit theorem for the position of the rightmost occupied site. Our approach is based on the construction of a sequence of renewal times, defined through a detailed analysis of active infection paths. These results are obtained in the supercritical regime of the Spont process.

math.PR↗