Large Deviations Performance of Interval Algorithm for Random Number Generation

| We investigate large deviations performance of the interval algorithm for random number generation, especially for intrinsic randomness. First, we show that the length of output fair random bits per the length of input sequence approaches to the entropy of the source almost surely. Next, we consider to obtain the xed number of fair random bits from the input sequence with xed length. We show that the approximation error measured by the variational distance and divergence vanishes exponentially as the length of input sequence tends to in nity, if the number of fair bits per input sample is below the entropy of the source. Contrarily, the approximation error measured by the variational distance approaches to two exponentially, if the number of fair bits per input sample is above the entropy. Keywords|random number generation, interval algorithm, intrinsic randomness, variational distance, error exponent, divergence.