The exact asymptotic of the time to collision

In this note we consider the time of the collision tau for n independent copies of Markov processes X-t(1), ...., X-t(n), each starting from x(i), where x(1) < ... < x(n). We show that for the continuos time random walk P-x(tau > t) = t(=n(n-1)/4)(Ch(x) + 0(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.