This paper studies the performance of ad hoc networks with local FDMA scheduling using stochastic point processes. In such networks, the Poisson assumption is not justified due to interdependencies between points introduced by scheduling. For this reason, an upper bound on the second reduced moment measure is derived. Using this result, two lower bounds on the success probability are given, based on the second order product density and a non-homogeneous Poisson approximation. The relative performance of local FDMA is compared to random channel access. It is shown that the relative outage probability reduction of local FDMA highly depends on the SIR threshold as well as on the ratio of transmission distance to orthogonalization distance. If these two quantities are small, the improvement is high; the number of channels has only a minor effect on the relative improvement.