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2005 The Exact Asymptotic of the Time to Collision
Zbigniew Puchala, Tomasz Rolski
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Electron. J. Probab. 10: 1359-1380 (2005). DOI: 10.1214/EJP.v10-291

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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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

Information

Accepted: 18 November 2005; Published: 2005
First available in Project Euclid: 1 June 2016

zbMATH: 1110.60069
MathSciNet: MR2183005
Digital Object Identifier: 10.1214/EJP.v10-291

Subjects:
Primary: 60J27
Secondary: 60J65

Keywords: Brownian motion , collision time , Continuous time random walk , skew Young tableaux , tandem queue

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