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. |