Random walks on higher-order networks

• Grant number: 25/27971-3
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: February 01, 2026
• End date: January 31, 2027
• Field of knowledge: Physical Sciences and Mathematics - Physics
• Principal Investigator: Guilherme Ferraz de Arruda
• Grantee: Gabriel Masqueti Simão
• Host Institution: Instituto de Física Gleb Wataghin (IFGW). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

Despite its simplicity, random walk is the most paradigmatic process and can be defined under many different assumptions. For example, we can have unbiased, maximum entropy, non-backtracking random walks, among many others. Despite its importance, this process has not been extensively studied in higher-order networks. Thus, the goal of this proposal is to systematically study random walks on higher-order networks, to reproduce the results in the literature, and to uncover important structural properties of such systems that may ultimately open new lines of research. By exploring these results, we also plan to propose random walk centrality measures to help characterize higher-order systems. In addition to the scientific results, the student is expected to become familiar with the scientific method and improve his/her academic skills in stochastic processes, linear algebra, and computational methods. (AU)