First-order limits, an analytical perspective

Jaroslav Nešetřil, Patrice Ossona de Mendez
2016 European journal of combinatorics (Print)  
In this paper we present a novel approach to graph (and structural) limits based on model theory and analysis. The role of Stone and Gelfand dualities is displayed prominently and leads to a general theory, which we believe is naturally emerging. This approach covers all the particular examples of structural convergence and it put the whole in new context. As an application, it leads to new intermediate examples of structural convergence and to a "grand conjecture" dealing with sparse graphs. We survey the recent developments.
doi:10.1016/j.ejc.2015.07.012 fatcat:bd5u5kga6fd3xioa6cpbqrpkny