suppose there is a set of vectors $S = \{ s_1, s_2, \cdots, s_n\}, s_i \in \mathbb{R}^2$.
the "random walk" I am interested in is to start at $(0, 0)$,
1, sample a step $s_i$ from $S$ with equal probability.
2, sample second step $s_j$ from $S\setminus \{s_i\}$ with equal probability.
3, repeat until all the steps have been enumerated.
Is there any field study on the properties of the trace of this type of "random walk"?
E.g. Expected position within $t$ steps. Convex hull density within $t$ steps.