# The energy of a deterministic Loewner chain: Reversibility and interpretation via SLE$_{0+}$

### Yilin Wang

ETH Zürich, Switzerland

## Abstract

We study some features of the energy of a deterministic chordal Loewner chain, which is defined as the Dirichlet energy of its driving function. In particular, using an interpretation of this energy as a large deviation rate function for SLE$_{κ}$ as $κ→0$ and the known reversibility of the SLE$_{κ}$ curves for small $κ$, we show that the energy of a deterministic curve from one boundary point $a$ of a simply connected domain $D$ to another boundary point $b$ is equal to the energy of its time-reversal, ie. of the same curve but viewed as going from $b$ to $a$ in $D$.

## Cite this article

Yilin Wang, The energy of a deterministic Loewner chain: Reversibility and interpretation via SLE$_{0+}$. J. Eur. Math. Soc. 21 (2019), no. 7, pp. 1915–1941

DOI 10.4171/JEMS/876