Math @ Duke

Publications [#339329] of Richard T. Durrett
Papers Published
 Cristali, I; Ranjan, V; Steinberg, J; Beckman, E; Durrett, R; Junge, M; Nolen, J, Block size in geometric(P)biased permutations,
Electronic Communications in Probability, vol. 23
(January, 2018),
pp. 110, Institute of Mathematical Statistics [doi]
(last updated on 2019/04/18)
Abstract: © 2018, University of Washington. All rights reserved. Fix a probability distribution p = (p1, p2, …) on the positive integers. The first block in a pbiased 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, ∞) are dry. For the geometric distribution pj = p(1 − p)j−1 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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