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The exact asymptotic of the time to collision. (English) Zbl 1110.60069

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.

MSC:

60J27 Continuous-time Markov processes on discrete state spaces
05E10 Combinatorial aspects of representation theory
60J65 Brownian motion
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