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Any ideas to implement in matlab..

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The Matlab implementation is best addressed in other places than Mathoverflow. As for how to simulate a random walk, it's not clear what you mean (what sort of steps are you taking in the random walk?). If you just want uniform samples from the polytope, see mathoverflow.net/questions/9854/…. – Henry Cohn Jan 22 2012 at 17:36

closed as not a real question by Igor Pak, Bill Johnson, Henry Cohn, Anthony Quas, S. Sra Jan 22 2012 at 20:37

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