Logarithmic fluctuations of Stationary Hastings-Levitov

Abstract

We prove that the fluctuation field $\{M_t(x){\}}_{x\in \mathbb{R}}$ of stationary Hastings-Levitov$(0)$ exhibits logarithmic spatial correlations. Moreover, by studying the infinitesimal generator of the imaginary part of $M_t(0)$, we show that for some $\beta >0$, ${\max }_{x\in [0,t]}\text{Im}{M}_t(x)<\beta \log t$ with high probability, as $t\to \infty$.

14 pages 4 figures