This paper derives exact finite-time maximum and minimum statistics for biased random walks, links the relaxation spectrum to the Marchenko-Pastur law of random matrices, and applies the results to molecular motors and sports scoring.
Kinetic characterization of heat bath and the energetics of thermal ratchet models,
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Extreme-Value Statistics of Stochastic Transport Processes: Applications to Molecular Motors and Sports
This paper derives exact finite-time maximum and minimum statistics for biased random walks, links the relaxation spectrum to the Marchenko-Pastur law of random matrices, and applies the results to molecular motors and sports scoring.