Laplace transform asymptotics and large deviation principles for longest success runs in Bernoulli trials. (September 2016) - Konstantopoulos, Takis
Abstract: The longest stretch L ( n ) of consecutive heads in n independent and identically distributed coin tosses is seen from the prism of large deviations. We first establish precise asymptotics for the moment generating function of L ( n ) and then show that there are precisely two large deviation principles, one concerning the behavior of the distribution of L ( n ) near its nominal value log1∕ p n and one away from it. We discuss applications to inference and to logarithmic asymptotics of functionals of L ( n ).