The Rademacher random walk associated with a deterministic sequence $(a_n)_{n \geq 1}$ is the walk which starts at zero and, at step $i$, independently steps either up or down by $a_i$ with equal probability. We will consider the following natural questions: what conditions on the growth rate of $(a_n)$ guarantee that the walk is transient? What growth conditions guarantee that the walk is weakly recurrent?

We will show that if the sequence is bounded, the walk is weakly recurrent, while if $a_n = n^{\alpha + o(1)}$ for some $\alpha > 1/2$, the walk is transient. We will also see that both of these results are in some sense tight.

The talk is based on joint work with Satyaki Bhattacharya and Ed Crane.