Meeting time distributions in Bernoulli systems

Details Meeting time distributions in Bernoulli systems Meeting time distributions in Bernoulli systems

2011-03-30

arxiv.org/abs/1103.5816v2

J. Phys. A: Math. Theor. 44 (2011) 375101

Nonlinear Sciences

Chaotic Dynamics

14 pages, 5 figures

Scientific paper

10.1088/1751-8113/44/37/375101

Meeting time is defined as the time for which two orbits approach each other within distance $\epsilon$ 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 $\epsilon\to0$, the distribution converges to exp(-\alpha\tau), where $\tau$ is the meeting time normalized by the average. The exponent is shown to be $\alpha=\sum_{l=1}^{k}p_l(1-p_l)$ for the Bernoulli systems.

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