The Exact Asymptotic of the Time to Collision
Zbigniew Puchala, Wroclaw University
Tomasz Rolski, Wroclaw University
Abstract
In this note we consider the time of the collision $tau$ for $n$ independent copies
of Markov processes $X^1_t,. . .,X^n_t$, each starting from $x_i$,where
$x_1 <. . .< x_n$. We show that for the continuous time random walk
$P_{x}(tau > t) = t^{-n(n-1)/4}(Ch(x)+o(1)),$ where $C$ is known and
$h(x)$ is the Vandermonde determinant. From the proof one can see that the
result also holds for $X_t$ being the Brownian motion or the Poisson process.
An application to skew standard Young tableaux is given.
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