The asymptotics of group Russian roulette
| Autor: | van de Brug, Tim, Kager, Wouter, Meester, Ronald |
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| Rok vydání: | 2015 |
| Předmět: | |
| Zdroj: | Markov Processes and Related Fields 23, 35-66 (2017) |
| Druh dokumentu: | Working Paper |
| Popis: | We study the group Russian roulette problem, also known as the shooting problem, defined as follows. We have $n$ armed people in a room. At each chime of a clock, everyone shoots a random other person. The persons shot fall dead and the survivors shoot again at the next chime. Eventually, either everyone is dead or there is a single survivor. We prove that the probability $p_n$ of having no survivors does not converge as $n\to\infty$, and becomes asymptotically periodic and continuous on the $\log n$ scale, with period 1. Comment: 26 pages, 1 figure; Mathematica notebook and output file (calculated exact bounds) are included with the source files |
| Databáze: | arXiv |
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