Aromi, Lloyd L.Katz, Yuri A.Vives i Santa Eulàlia, Josep, 1963-2023-02-202023-08-142021-08-141007-5704https://hdl.handle.net/2445/193830Topological data analysis provides a new perspective on many problems in the domain of complex systems. Here, we establish the dependency of mean values of functional $p$ norms of 'persistence landscapes' on a uniform scaling of the underlying multivariate distribution. Furthermore, we demonstrate that average values of $p$-norms are decreasing, when the covariance in a system is increasing. To illustrate the complex dependency of these topological features on changes in the variance-covariance matrix, we conduct numerical experiments utilizing bi-variate distributions with known statistical properties. Our results help to explain the puzzling behavior of $p$-norms derived from daily log-returns of major equity indices on European and US markets at the inception phase of the global financial meltdown caused by the COVID-19 pandemic.application/pdfengcc-by-nc-nd (c) Elsevier B.V., 2021https://creativecommons.org/licenses/by-nc-nd/4.0/Processos estocàsticsEstadísticaGrups topològicsHomologiaStochastic processesStatisticsTopological groupsHomologyinfo:eu-repo/semantics/article7208372023-02-20info:eu-repo/semantics/openAccess