The Maximum of a Random Walk and Its Application to Rectangle Packing

Abstract : We consider a symmetric random walk of length $n$ that starts at the origin and takes steps uniformly distributed on the real interval $[-1,+1]$. We study the large-$n$ behavior of the expected maximum excursion and prove a very precise estimate. 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 when the rectangle sides are $2n$ independent uniform random draws from $[0,1]$.
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Submitted on : Wednesday, May 24, 2006 - 12:55:53 PM
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E.G. Coffman, Philippe Flajolet, Leopold Flatto, Micha Hofri. The Maximum of a Random Walk and Its Application to Rectangle Packing. [Research Report] RR-3223, INRIA. 1997. ⟨inria-00073466⟩

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