The exact asymptotic of the time to collision

Author Puchała Z.; Rolski T.
Title The exact asymptotic of the time to collision
Journal Electronic Journal of Probability
Year 2005
Status Published
Volume 10
Pages 1359–1380
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 $x_1 t) = t^{-n(n-1)/4}(Ch(x)+o(1)),$ 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.