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Scanning probes can be used for storage of data at ultra-high areal densities, beyond those achieved by other techniques. Thermo-mechanical probe storage is one variant of scanning-probe technology in which data is stored in the form of indentations in thin polymer films. A simplified channel model of thermo-mechanical probe storage is first introduced, derived from a comprehensive characterization study of experimentally extracted read-back signals. This model is then used as basis for deriving analytical expressions for the probability density function of the storage channel output signal in the presence of stochastic impairments such as noise and jitter. These expressions are used to construct an optimal bit-by-bit channel detector and to derive a theoretical formula for its bit error rate. Finally, the results of the analytical study are validated by comparison with simulation results. Analytical expressions for the channel output statistics are valuable as they enable quick performance comparisons between candidate detection schemes without resorting to lengthy simulations. Furthermore, they can be used to design probabilistic/soft detectors for soft-input error-correction schemes.