4 problems

Let $(n_k)_{k\geq 1}$ be a Hadamard lacunary sequence, meaning that there is a constant $q>1$ such that $n_{k+1}/n_k\geq q$ for all $k$. For $N\geq 1$, let $D_N(\{n_kx\})$ denote t…

Nominal-time finite LIL bounds are bounds for independent 1-sub-Gaussian observations expressed in terms of nominal time $t$, rather than intrinsic time $V_t$. Scaling conjecture.…

Let $(n_k)_{k\geq 1}$ be a lacunary sequence, and consider the almost independent system $(\{n_kx\})_{k\geq 1}$ for almost every $x$. The Chung–Smirnov law of the iterated logarith…

Let $Y_0,Y_1,\ldots$ be independent uniformly distributed random variables on the unit square, let $\boldsymbol{\Phi}$ be the area-preserving Lambert map from the square to…