Dichotomy results for eventually always hitting time statistics and almost sure growth of extremes

Mark Holland, Maxim Kirsebom, Philipp Kunde +1

Suppose $(f,\mathcal{X},\mu )$ is a measure preserving dynamical system and $\varphi :\mathcal{X}\to \mathbb{R}$ a measurable function. Consider the maximum process $M_n:=\max\{X_1 \l…