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We examined the transition parameter and position jitter in perpendicular media by micromagnetic simulations that included thermal fluctuations. We observed the effects of grain size, intergranular exchange, anisotropy distributions, and orientation distributions. All these parameters affected both the transition parameter and the M-H loop coercivity squareness (S*). The net effect was a universal dependence of transition parameter on S*. The position jitter normalized by the grain diameter decreased with increasing S*, but a universal curve was not found. In general, a small grain diameter, moderate exchange and low anisotropy distribution increase the high-density signal-to-noise ratio.