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arXiv · 2510.20520

Asymptotic versus mesoscopic spectral dimensions in networks and inhomogeneous structures

Lorenzo Grimaldi·Pablo Villegas·Alessandro Vezzani·Raffaella Burioni·Davide Cassi·Andrea Gabrielli
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Abstract

"Every object that biology studies is a system of systems." (Fran\c{c}ois Jacob, 1974). Most networks feature intricate architectures originating from tinkering, a repetitive use of existing components where structures are not invented but reshaped. Linking the properties of primitive components to the emergent behavior of composite networks remains a key open challenge. Here, we show that modular compositions generically decouple the spectral and Fiedler dimensions, so that networks with identical thermodynamic exponents can exhibit parametrically different equilibration dynamics.

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Lorenzo Grimaldi, Pablo Villegas, Alessandro Vezzani, Raffaella Burioni, Davide Cassi, Andrea Gabrielli. 2025-10-23. Asymptotic versus mesoscopic spectral dimensions in networks and inhomogeneous structures. https://doi.org/10.1103/zdpg-dr6t

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