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The Exact Asymptotic of the Time to Collision

   
@article{EJP291,
	author = {Zbigniew Puchala and Tomasz Rolski},
	title = {The Exact Asymptotic of the Time to Collision},
	journal = {Electron. J. Probab.},
	fjournal = {Electronic Journal of Probability},
	volume = {10},
	year = {2005},
	keywords = {continuous time random walk; Brownian motion; collision time; skew Young tableaux; tandem queue},
	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.},
	pages = {no. 40, 1359-1380},
	issn = {1083-6489},
	doi = {10.1214/EJP.v10-291},    
        url = {http://ejp.ejpecp.org/article/view/291}}