tightness results for infinite slit limits of the chordal loewner equation

• DOI: 10.48550/arxiv.1608.04084
• Publication Date: 2017-05-25
• Authors: Andrea del Monaco; Ikkei Hotta; Sebastian Schleiß...
• Keywords: Mathematics - Complex Variables; Probability (math.PR); FOS: Mathematics; Complex Variables (math.CV); Mathematics - Probability

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 provides a measure valued process $t\mapsto \{��_{N,t}\},$ and we are interested in the limit behaviour as $N\to\infty.$ We prove tightness of the sequence $\{��_{N,t}\}_{N\in\mathbb{N}}$ under certain assumptions and address some further problems.