The exact asymptotic of the time to collision

TitleThe exact asymptotic of the time to collision
Publication TypeJournal Article
Year of Publication2005
AuthorsPuchała Z, Rolski T.
JournalElectronic Journal of Probability
Volume10
Pagination1359–1380
Date Published11
AbstractAbstract 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 $x_1 t) = t^{-n(n-1)/4}(Ch(x)+o(1)),$ 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.