Lukas Schoug

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math.PR2022

Conformal removability of SLE $_{4}$

Konstantinos Kavvadias, Jason Miller, Lukas Schoug

We consider the Schramm-Loewner evolution (SLE $_{κ}$ ) with $κ = 4$ , the critical value of $κ > 0$ at or below which SLE $_{κ}$ is a simple curve and above which it is self-intersecting. We…

math.PR2019

Dimension of two-valued sets via imaginary chaos

Lukas Schoug, Avelio Sepúlveda, Fredrik Viklund

Two-valued sets are local sets of the two-dimensional Gaussian free field (GFF) that can be thought of as representing all points of the domain that may be connected to the boundar…

math.PR2019

A multifractal boundary spectrum for SLE $_{κ} (ρ)$

Lukas Schoug

We study SLE $_{κ} (ρ)$ curves, with $κ$ and $ρ$ chosen so that the curves hit the boundary. More precisely, we study the sets on which the curves collide with the boundary at a prescr…

Conformal removability of SLE4​

Dimension of two-valued sets via imaginary chaos

A multifractal boundary spectrum for SLEκ​(ρ)

Conformal removability of SLE $_{4}$

A multifractal boundary spectrum for SLE $_{κ} (ρ)$