The first of N i.i.d. Brownian trajectories that arrive at a small target sets a time scale which is much shorter than that of the arrival of a typical trajectory. The shortest arrival time is computed here analytically in an asymptotic approximation for large N. The asymptotic expression is computed here based on the short-time asymptotics of the pdf of the first time to a small target in 1, 2 and 3 dimensions. These are referred to in the statistical physics literature as extreme statistics.
|Title of host publication||Applied Mathematical Sciences (Switzerland)|
|Number of pages||30|
|State||Published - 2018|
|Name||Applied Mathematical Sciences (Switzerland)|