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

We provide a complete thermodynamic solution of a 1D hopping model in the presence of a random potential by obtaining the density of states. Since the partition function is related to the density of states by a Laplace transform, the density of states determines completely the thermodynamic behavior of the system. We have also shown that the transfer matrix technique, or the so-called dynamic programming, used to obtain the density of states in the 1D hopping model may be generalized to tackle a long-standing problem in statistical significance assessment for one of the most important {\em proteomic} tasks - - peptide sequencing using tandem mass spectrometry data.