  Let S_i be a random walk with standard exponential increments. We call
\sum_{i=1}^k S_i its k-step area. The random variable V = \inf_{k \ge 1}
\frac{2}{k(k+1)} \sum_{i=1}^k S_i plays important role in the study of
so-called one-dimensional sticky particles model. We find the distribution of V
and prove that P(V > t) = \sqrt{1-t} exp(-t/2) for t in [0,1]. We also show
that the variables \min_{1 \le k \le n} \frac{2n}{k(k+1)} \sum_{i=1}^k U_{i, n}
converge in distribution to V. Here U_{i, n} are the order statistics of n
i.i.d. random variables uniformly distributed on [0,1].

Probability