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Random unfriendly seating arrangement in a dining table |
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| Institution: | 1. Department of Computer Science, National Taiwan Ocean University, Keelung 202, Taiwan;2. Institute of Statistical Science, Institute of Information Science, Academia Sinica, Taipei 115, Taiwan;3. Institute of Statistical Science, Academia Sinica, Taipei 115, Taiwan |
| Abstract: | A detailed study is made of the number of occupied seats in an unfriendly seating scheme with two rows of seats. An unusual identity is derived for the probability generating function, which is itself an asymptotic expansion. The identity implies particularly a local limit theorem with optimal convergence rate. Our approach relies on the resolution of Riccati equations. We also clarify some simple yet delicate stochastic dominance relations. |
| Keywords: | Riccati equation Jamming density Quasi-power theorem Central and local limit theorem Stochastic dominance |
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