Quasi-Sure Stochastic Analysis through Aggregation and SLE$_κ$ Theory

We study SLE$_κ$ theory with elements of Quasi-Sure Stochastic Analysis through Aggregation. Specifically, we show how the latter can be used to construct the SLE$_κ$ traces quasi-surely (i.e. simultaneously for a family of probability measures with certain properties) for $κ\in \mathcal{K}\cap \mathbb{R}_+ \setminus ([0, ε) \cup \{8\})$, for any $ε>0$ with $\mathcal{K} \subset \mathbb{R}_{+}$ a nontrivial compact interval, i.e. for all $κ$ that are not in a neighborhood of zero and are different from $8$. As a by-product of the analysis, we show in this language a version of the continuity in $κ$ of the SLE$_κ$ traces for all $κ$ in compact intervals as above.

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