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In this note, we consider a multi-slit Loewner equation with constant coefficients that describes the growth of multiple SLE curves connecting N points on \(\mathbb {R}\) to infinity within the upper half-plane. For every \(N\in \mathbb {N}\), this equation yields a measure-valued process \(t\mapsto \{\alpha _{N,t}\},\) and we are interested in the limit behaviour as \(N\rightarrow \infty .\) We prove tightness of the sequence \(\{\alpha _{N,t}\}_{N\in \mathbb {N}}\) under certain assumptions and address some further problems. Moreover, we investigate a similar situation in which all slits are trajectories of a certain quadratic differential.

Tightness Results for Infinite-Slit Limits of the Chordal Loewner Equation