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Exact Distribution of the Maximal Height of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>p</mml:mi></mml:math>Vicious Walkers
Using path-integral techniques, we compute exactly the distribution of the maximal height ${H}_{p}$ of $p$ nonintersecting Brownian walkers over a unit time interval in one dimension, both for excursions $p$ watermelons with a wall, and bridges $p$ watermelons without a wall, for all integer $p\ensuremath{\ge}1$. For large $p$, we show …