Scholarly Works  Pure Mathematics and Mathematical Statistics
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Almost sure multifractal spectrum of SLE
Suppose that $\eta$ is a SchrammLoewner evolution (SLE$_\kappa$) in a smoothly bounded simply connected domain $D \subset {\mathbb C}$ and that $\phi$ is a conformal map from ${\mathbb D}$ to a connected component of $D ... 
Brownian motion correlation in the peanosphere for $κ> 8$
The peanosphere (or "mating of trees") construction of Duplantier, Miller, and Sheffield encodes certain types of $\gamma$Liouville quantum gravity (LQG) surfaces ($\gamma \in (0,2)$) decorated with an independent ... 
The structure theory of Nilspaces II: Representation as nilmanifolds
This paper forms the second part of a series by the authors [GMV1,GMV3] concerning the structure theory of nilspaces of Antol\'in Camarena and Szegedy. A nilspace is a compact space $X$ together with closed collections of ... 
Selfavoiding walks and amenability
The connective constant $\mu(G)$ of an infinite transitive graph $G$ is the exponential growth rate of the number of selfavoiding walks from a given origin. The relationship between connective constants and amenability ...