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.
Citation
Zbigniew Puchala. Tomasz Rolski. "The Exact Asymptotic of the Time to Collision." Electron. J. Probab. 10 1359 - 1380, 2005. https://doi.org/10.1214/EJP.v10-291
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