Tracy-Widom Distribution and its Applications
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چکیده
Example : (Local maxima) Let Z = (Z1, ..., Zn) be i.i.d. U(0, 1) random variables and let Sn be the number of local maxima in Z. Then Sn/ √ V ar(Sn)→d N (0, 1) as n→∞. CLT is so strong due to its universality and a natural question is whether there are other laws that own the same property. Tracy-Widom distribution and its variants form such a class and they appear in several statistics of random permutations, queue theory, random matrices, percolation, and many others.
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تاریخ انتشار 2014