  The comprehensive simulation of magnetic recording, including the write and
read-back process, on granular media becomes computationally expensive if the
magnetization dynamics of each grain are explicitly computed. In addition, in
heat-assisted magnetic recording, the writing of a single track becomes a
random process since the temperature must be considered and thermal noise is
involved. Further, varying grain structures of various granular media must also
be taken into account to obtain correct statistics for the final read-back
signal. Hence, it requires many repetitions of the write process to investigate
the mean signal as well as the noise. This work presents a method that improves
the statistical evaluation of the whole recording process. The idea is to avoid
writing the magnetization to one of its binary states. Instead, we assign each
grain its probability of occupying one of its stable states, which can be
calculated in advance in terms of a switching probability phase diagram. In the
read-back process, we combine the probabilities to calculate a mean signal and
its variance. Afterwards, repetitions on different media lead to the final
read-back signal. Using a recording example, we show that the statistical
behavior of the evaluated signal-to-noise ratio can be significantly improved
by applying this probability mapping method, while the computational effort
remains low.
