Abstract
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.
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Holcman, D., Schuss, Z. (2018). Short-Time Asymptotics of the Heat Kernel and Extreme Statistics of the NET. In: Asymptotics of Elliptic and Parabolic PDEs. Applied Mathematical Sciences, vol 199. Springer, Cham. https://doi.org/10.1007/978-3-319-76895-3_9
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DOI: https://doi.org/10.1007/978-3-319-76895-3_9
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Publisher Name: Springer, Cham
Print ISBN: 978-3-319-76894-6
Online ISBN: 978-3-319-76895-3
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