Timeline for How is the longest increasing subsequence a matrix integral?
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| Dec 12, 2010 at 19:32 | comment | added | Leonid Petrov | John: Depends on the statistic. I believe that for most combinatorial properties of permutations you need there is some correspondence. E.g., for cycles the reasonable way is to consider corresponding partitions of the set {1,..,n} and then reduce this also to partitions, for uniform random permutations this has much to do with Poisson-Dirichlet distributions. RS correspondence is another correspondence of this sort. It is very natural when you consider representations of symmetric groups. | |
| Dec 12, 2010 at 11:28 | comment | added | john mangual | What if I'm not looking for increasing subsequences. What if I want to count cycles, fixed points or some other statistic? I wonder what makes RS correspondence so fundamental. | |
| Dec 12, 2010 at 11:25 | comment | added | Leonid Petrov | Well, we started from "permutations-matrices" connection, I suggest "permutations-partitions-matrices", and now I see that the two "matrices" here are quite different. The first is about uniform measures on compact classical groups, and the second is about random matrices (i.e., Gaussian Unitary Ensemble, etc.). So here I say "no" to your comment. | |
| Dec 12, 2010 at 11:15 | comment | added | Gerry Myerson | Does doing "On the other hand" twice get you back to the hand you started on? | |
| Dec 12, 2010 at 7:56 | history | answered | Leonid Petrov | CC BY-SA 2.5 |