Puchała, Zbigniew; Rolski, Tomasz The exact asymptotic of the time to collision. (English) Zbl 1110.60069 Electron. J. Probab. 10, Paper No. 40, 1359-1380 (2005). Summary: 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 \(\mathbf P_{x}(\tau > t) = t^{-n(n-1)/4}(Ch(x)+o(1)),\) 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. Cited in 3 Documents MSC: 60J27 Continuous-time Markov processes on discrete state spaces 05E10 Combinatorial aspects of representation theory 60J65 Brownian motion PDFBibTeX XMLCite \textit{Z. Puchała} and \textit{T. Rolski}, Electron. J. Probab. 10, Paper No. 40, 1359--1380 (2005; Zbl 1110.60069) Full Text: EuDML