  We study the distribution (w.r.t. the vacuum state) of family of partial sums
Sm of position operators on weakly monotone Fock space. We show that any single
operator has the Wigner law, and an arbitrary family of them (with the index
set linearly ordered) is a collection of monotone independent random variables.
It turns out that our problem equivalently consists in finding the m-fold
monotone convolution of the semicircle law. For m = 2 we compute the explicit
distribution. For any m > 2 we give the moments of the measure, and show it is
absolutely continuous and compactly supported on a symmetric interval whose
endpoints can be found by a recurrence relation.
