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<XML><RECORDS>
<RECORD>
	<REFERENCE_TYPE>0</REFERENCE_TYPE>
	<AUTHORS>
		<AUTHOR>Pucha{\l}a, Z.</AUTHOR>
		<AUTHOR>Rolski, T.</AUTHOR>
	</AUTHORS>
	<YEAR>2005</YEAR>
	<TITLE>The exact asymptotic of the time to collision</TITLE>
	<SECONDARY_TITLE>Electronic Journal of Probability</SECONDARY_TITLE>
	<VOLUME>10</VOLUME>
	<NUMBER>Probab</NUMBER>
	<PAGES>1359-1380</PAGES>
	<DATE>11</DATE>
	<KEYWORDS>
		<KEYWORD>continuous time random walk</KEYWORD>
		<KEYWORD>Brownian motion</KEYWORD>
		<KEYWORD>Collision time</KEYWORD>
		<KEYWORD>skew Young tableaux</KEYWORD>
		<KEYWORD>tandem queue</KEYWORD>
		<KEYWORD>Probability Theory</KEYWORD>
		<KEYWORD>Stochastic Processes</KEYWORD>
	</KEYWORDS>
	<ABSTRACT>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 $x_1 &lt;. . .&lt; x_n$. We show that for the continuous time random walk $P_x(tau &gt; t) = t^-n(n-1)/4(Ch(x)+o(1)),$ 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. </ABSTRACT>
	<URL>http://www.math.washington.edu/~ejpecp/viewarticle.php?id=1551&amp;layout=abstract</URL>
</RECORD>
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