Jaroslav Nešetřil, Patrice Ossona de Mendez
Local-global convergence, an analytic and structural approach

Comment.Math.Univ.Carolin. 60,1 (2019) 97-129.

Abstract:Based on methods of structural convergence we provide a unifying view of local-global convergence, fitting to model theory and analysis. The general approach outlined here provides a possibility to extend the theory of local-global convergence to graphs with unbounded degrees. As an application, we extend previous results on continuous clustering of local convergent sequences and prove the existence of modeling quasi-limits for local-global convergent sequences of nowhere dense graphs.

Keywords: structural limit; Borel structure; modeling; local-global convergence

DOI: DOI 10.14712/1213-7243.2015.280
AMS Subject Classification: 03C13 03C98 05C99