Capture of particles and distribution of the maximum of a one-dimensional random walk.
(Joint work with S. Majumdar and R. M. Ziff)
Two random-walk related problems, which have been studied independently in the past, the expected maximum of a random walk in 1D and the flux to a spherical trap of particles undergoing discrete jumps in 3D, are shown to be closely related to each other and are studied using a unified approach as a solution to a Wiener-Hopf problem.
For the flux problem, we show that a constant c=0.29795219 which appeared in the context of the boundary extrapolation length, and was previously found numerically, can be derived analytically. The same constant enters in the higher-order corrections to the expected maximum asymptotics.