First passages in bounded domains: when is the mean first passage time meaningful?

@article{Mattos2012FirstPI,
title={First passages in bounded domains: when is the mean first passage time meaningful?},
author={Thiago G Mattos and Carlos Mej{\'i}a-Monasterio and Ralf Metzler and Gleb Oshanin},
journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
year={2012},
volume={86 3 Pt 1},
pages={
031143
}
}

We study the first passage statistics to adsorbing boundaries of a Brownian motion in bounded two-dimensional domains of different shapes and configurations of the adsorbing and reflecting boundaries. From extensive numerical analysis we obtain the probability P(ω) distribution of the random variable ω=τ(1)/(τ(1)+τ(2)), which is a measure for how similar the first passage times τ(1) and τ(2) are of two independent realizations of a Brownian walk starting at the same location. We construct a… CONTINUE READING