Papers Published
Abstract:
Fix a probability distribution p = (p1, p2, ā¦) on the positive integers. The first block in a p-biased permutation can be visualized in terms of raindrops that land at each positive integer j with probability pj. It is the first point K so that all sites in [1, K] are wet and all sites in (K, ā) are dry. For the geometric distribution pj = p(1 ā p)jā1 we show that p log K converges in probability to an explicit constant as p tends to 0. Additionally, we prove that if p has a stretch exponential distribution, then K is infinite with positive probability.