Meeting time distributions in Bernoulli systems

Abstract

Meeting time is defined as the time for which two orbits approach each other within distance $\hat{I}\mu$ 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 $\hat{I}\mu \to 0$, the distribution converges to exp(-ατ), where $\ddot{I}„$ is the meeting time normalized by the average. The exponent is shown to be $\hat{I}\pm ={\sum }_{l=1}^k{p}_l(1-p_l)$ for the Bernoulli systems.

14 pages, 5 figures