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
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