Random Volumes in the n-Cube

نویسندگان

  • Martin E. Dyer
  • Zoltán Füredi
  • Colin McDiarmid
چکیده

Consider lhe rr-cube [0. l]" in R'. This has l" r'ertices and volume I. Pick .\' = .\'(r) r'erlices indcpendentll' a1 random. form their convex hull. and let I'n be its expected volume. Hor"'large should ,\'(rt) be to pick up significant volume? Ler r = 2l"Q x I.213. and let r > 0. We have rc-cenlll' shown that. ds n-t-.1;-0 if .\'(r)< (,(-r)'.and I,-I it.\'(n)>\r+r)'. We discuss this and related results.

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تاریخ انتشار 1990