Winning the Hand of the Princess Saralinda
نویسنده
چکیده
Suitors come to the castle in order to try to win the hand of the Princess Saralinda. The first suitor to perform n amazing feats will succeed. If the number n of feats is large and the times to perform the feats are all i.i.d., then how long is it before a suitor will win the hand of the Princess? We develop asymptotics describing the distribution of this random time as the number of feats gets large; e.g., we show that this time is of order nm−σ √ n logn, where m and σ are the mean and variance of the time to perform a single feat, provided that the time to perform a single feat has a finite moment generating function and the suitor arrival process obeys a strong law of large numbers. The −√logn term reflects the fact that there is an arrival process of suitors instead of just one. The asymptotic effect of the arrival process is equivalent to having α √ n suitors present at time 0 with no additional arrivals. We also obtain large deviations results that depend on the full interarrival-time distribution.
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