Spectral convergence of Laplacians on dense hypergraph sequences

Datum

11.12.2025

Zeit

15:00 - 16:00

Sprecher

Sjoerd Van der Niet

Zugehörigkeit

Renyi Institute Budapest, TU Munich

Sprache

en

Hauptthema

Biologie

Host

Local Organisers: Nikola Sadovek, Maximilian Wiesmann, Giulio Zucal

Beschreibung

Higher-order networks have become a popular tool in the network science community to model dynamics such as synchronization and diffusion. The linearized system often depends on a Laplacian operator and its spectral properties. We introduce a Laplacian operator for uniform hypergraphs and study the limiting operator for an increasing sequence of dense uniform hypergraphs using the theory of graph limits. Although a theory of dense hypergraph limits has been developed by Elek and Szegedy, and independently Zhao, not much of its implications to spectral properties is known. We show that a weaker notion of convergence for the sequence of hypergraphs is sufficient to obtain pointwise convergence of the spectrum of the Laplacians.

Letztmalig verändert: 08.12.2025, 07:35:16