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The Exact Asymptotic of the Time to Collision


 
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1. Title Title of document The Exact Asymptotic of the Time to Collision
 
2. Creator Author's name, affiliation, country Zbigniew Puchala; Wroclaw University
 
2. Creator Author's name, affiliation, country Tomasz Rolski; Wroclaw University
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) continuous time random walk; Brownian motion; collision time; skew Young tableaux; tandem queue
 
3. Subject Subject classification 60J27; 60J65
 
4. Description 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.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) partially supported by KBN Grant No 2 P03A 020 23 (2002-2004)
 
7. Date (YYYY-MM-DD) 2005-11-18
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/291
 
10. Identifier Digital Object Identifier 10.1214/EJP.v10-291
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 10
 
12. Language English=en
 
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