In this paper, we consider the frequency reuse issue in the downlink of a multi-cell OFDMA system. We first implement the static frequency reuse scheme in the OFDMA sub-carrier assignment over the multi-cell system in order to control the inter-cell interference. Then, we add the random access sub-band to adopt the dynamic frequency reuse. The main purpose of introducing the random access sub-band is to improve the fairness of the system. In order to efficiently share the random access sub-band over the multi-cell sectors, the sector load information is considered. We assume that there is only a minimal coordination between the sectors so the central network controller provides only the access probabilities to each cell. With these probabilities, the sectors transmit the data on the random access channel. By doing so, the usage of the random access sub-band is randomized, and the fairness across the sector is provided by controlling the probabilities. Simulation results show that the proposed random access scheme achieve a performance improvement in the cell-edge user throughput.