Math @ Duke
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Publications [#339330] of James H. Nolen
Papers Published
- Nolen, JH; Cristali, I; Ranjan, V; Steinberg, J; Beckman, E; Durrett, R; Junge, M, Block size in Geometric(p)-biased permutations,
Electronic Communications in Probability, vol. 23
(2018),
pp. 1-10, Institute of Mathematical Statistics [doi]
(last updated on 2024/04/24)
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.
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