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We provide a complete thermodynamic solution of a 1D hopping model in thepresence of a random potential by obtaining the density of states. Since thepartition function is related to the density of states by a Laplace transform,the density of states determines completely the thermodynamic behavior of thesystem. We have also shown that the transfer matrix technique, or the so-calleddynamic programming, used to obtain the density of states in the 1D hoppingmodel may be generalized to tackle a long-standing problem in statisticalsignificance assessment for one of the most important proteomic tasks - peptidesequencing using tandem mass spectrometry data.

Statistical Characterization of a 1D Random Potential Problem - with applications in score statistics of MS-based peptide sequencing