Multiple SLE type scaling limits: from local to global

Understand

We consider collections of $N$ chordal random curves obtained from a critical lattice model on a planar graph, in the limit when a fine-mesh graph approximates a simply-connected domain.

• We define and study candidates for such limits in terms of conformally invariant collections of random curves, generated via iterated Loewner equations.
• These curves are a natural ``domain Markov extension'' of the earlier introduced local multiple SLE initial segments to global multiple SLE curves.
• For realizing them as scaling limits, we provide two a priori results to guarantee the precompactness of the discrete random curves and to allow promoting a discrete domain Markov property to the scaling limit.