Convergence and limits of finite trees

Abstract: Seeing the success of limit theory of dense finite graphs with graphons as their limit objects we developed a similar (?) theory for finite trees. In order for the sampling limit to make sense we need to make the trees "dense" - we do this by considering them as metric spaces with the normalized graph distance. Using ultaproducts is a simple and elegant way to find unique limit objects (we call them dendrons) and also to highlight similarities and major differences from the theory of dense graph limits. For the underlying quantitative approximation results, one needs more "down to earth" techniques to be developed. This is joint work with Gábor Elek.

combinatorics

Audience: researchers in the topic

Warwick Combinatorics Seminar

Series comments: This is the online combinatorics seminar at Warwick.