# Local limits for permutations and generating trees

## Location

For large combinatorial structures, two main notions of convergence can be defined: scaling limits and local limits. In particular, for graphs both notions are well-studied and well-understood. For permutations only a notion of scaling limits, called *permutons*, has been investigated in the last decade.

In the first part of the talk, we introduce a new notion of local convergence for permutations and we prove some characterizations in terms of proportions of *consecutive* pattern occurrences.

In the second part of the talk, we investigate a new method to establish local limits for pattern-avoiding permutations using *generating trees*. The theory of generating trees has been widely used to enumerate families of combinatorial objects, in particular permutations. The goal of this talk is to introduce a new facet of generating trees encoding families of permutations, in order to establish probabilistic results instead of enumerative ones.