Self-Avoiding Walks on Random Quadrangulations

The local limit of random quadrangulations (UIPQ) and the local limit of quadrangulations with a simple boundary (the simple boundary UIHPQ) are two very well studied objects. We shall see how the simple boundary UIHPQ relates to an annealed model of self-avoiding walk on random quadrangulations, and how metric information obtained for the UIHPQ can be used to study quantities such as the displacement of the self-avoiding walk from the origin, as well as to ultimately investigate how the biasing of random quadrangulations by the number of their self-avoiding walks affects their local limit.