Work

Random walks across dimensions: Exploring simplicial complexes

Year: 2026

Type: article

Abstract: We introduce an operator to describe a random walk process on a simplicial complex. Walkers are allowed to wander across simplices of various dimensions, bridging nodes to edges, and edges to triangles, via a nested organization that hierarchically extends to higher structures of arbitrarily large, but finite, dimension. The asymptotic distribution of the walkers provides a natural ranking to gauge the relative importance of higher-order simplices. Optimal search strategies in the presence of stochastic teleportation are addressed, and the peculiar interplay of noise with higher-order structures is unraveled.

Source: Physical review. E

DOI: 10.1103/ppm1-mxhz

Authors: Diego Febbe, Duccio Fanelli, Timoteo Carletti

Institutions: University of Namur, Istituto Nazionale di Fisica Nucleare, Namur Institute for Complex Systems, University of Florence

Language: English

Topic: Complex Network Analysis Techniques

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: hybrid

Funders: Ministero dell'Università e della Ricerca, NextGenerationEU

Awards: G2580906954, G5766285997