Meeting time distributions in Bernoulli systems

Meeting time is defined as the time for which two orbits approach each other within distance $ε$ in phase space. We show that the distribution of the meeting time is exponential in $(p_1,...,p_k)$-Bernoulli systems. In the limit of $ε\to0$, the distribution converges to exp(-ατ), where $τ$ is the meeting time normalized by the average. The exponent is shown to be $α=\sum_{l=1}^{k}p_l(1-p_l)$ for the Bernoulli systems.

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