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Craig A. Tracy Joint work with Harold Widom

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Marginal Distributions<br />

P(x m (t)≤x)<br />

Case m=1:<br />

Fix x 1 =x, sum P Y (X;t) over allowed x 2 , x 3 , x 4 ,...<br />

Can do this since contours are small: |ξ i |< 1<br />

Result is an expression involving N! terms. Use<br />

first miraculous identity to reduce sum to one<br />

term!<br />

Here’s the identity:<br />

Sunday, March 29, 2009<br />

18

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