Extreme-Value Statistics of Molecular Motors

Alexandre Guillet, Édgar Roldán, Frank Jülicher

Published 2019-08-09Version 1

We derive exact expressions for the finite-time statistics of extrema (maximum and minimum) of the spatial displacement and the fluctuating entropy flow of biased random walks modelling the dynamics of molecular motors at the single-molecule level. Our results generalize the infimum law for entropy production and reveal a symmetry of its distribution of maxima and minima, which are confirmed by numerical simulations of stochastic models of molecular motors. We also show that the relaxation spectrum of the full generating function, and hence of any momentum, of the finite-time extrema distributions can be written in terms of the Marcenko-Pastur distribution of random-matrix theory. Using this result, we obtain efficient estimates for the extreme-value statistics of molecular motors from the eigenvalue distributions of suitable Wishart and Laguerre random matrices.