dc.contributor.author Coffman, Edward G.Flajolet, PhilippeHofri, MichaLeopold, Flatto 2017-08-02T22:03:32Z 2017-08-02T22:03:32Z 1997-07-28 https://hdl.handle.net/1911/96468 Let S0,...,Sn be a symmetric random walk that starts at the origin (S0 = 0), and takes steps uniformly distributed on [-1,+1]. We study the large-n behavior of the expected maximum excursion and prove the estimate \exd \max_{0 \leq k \leq n} S_k = \sqrt{\frac{2n}{3\pi}} c +\frac{1}{5}\sqrt{\frac{2}{3\pi}} n^{-1/2} + O(n^{-3/2}), where c = 0.297952... This estimate applies to the problem of packing n rectangles into a unit-width strip; in particular, it makes much more precise the known upper bound on the expected minimum height, n/4 + 1/2 \exd \max_{0 \leq j \leq n} S_j + 1/2 = n/4 +O(n^(1/2)),\$ when the rectangle sides are 2n independent uniform random draws from [0,1]. 14 pp eng You are granted permission for the noncommercial reproduction, distribution, display, and performance of this technical report in any format, but this permission is only for a period of forty-five (45) days from the most recent time that you verified that this technical report is still available from the Computer Science Department of Rice University under terms that include this permission. All other rights are reserved by the author(s). The Maximum of a Random Walk and Its Application to Rectangle Packing Technical report July 28, 1997 TR97-283 Text Coffman, Edward G., Flajolet, Philippe, Hofri, Micha, et al.. "The Maximum of a Random Walk and Its Application to Rectangle Packing." (1997) https://hdl.handle.net/1911/96468.
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