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Bounty Ended with no winning answer by John Jiang
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John Jiang
John Jiang
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edge distribution of random young diagramYoung's tableaux from Okounkov's "random matrices and random permutations"

I am reading the paper "random matrices and random permutations""random matrices and random permutations" by Andrei Okounkov, which is very beautifully written. I just have several technical questions about some of the computations:

  1. in section 2.1.2, why is it clear that only the eigenvalues near the edges of the Wigner's semicircle contribute to the asymptotics of (2.1)? In the same spirit, on page 8, section 2.1.3, the author claims that it is easy to see that by taking a suitable linear combination we can single out hte contribution of only the maximal eigenvalues in formula (2.1). I don't quite see how a winner takes all argument can be applied.

edge distribution of random young diagram

I am reading the paper "random matrices and random permutations" by Andrei Okounkov, which is very beautifully written. I just have several technical questions about some of the computations:

  1. in section 2.1.2, why is it clear that only the eigenvalues near the edges of the Wigner's semicircle contribute to the asymptotics of (2.1)? In the same spirit, on page 8, section 2.1.3, the author claims that it is easy to see that by taking a suitable linear combination we can single out hte contribution of only the maximal eigenvalues in formula (2.1). I don't quite see how a winner takes all argument can be applied.

edge distribution of random Young's tableaux from Okounkov's "random matrices and random permutations"

I am reading the paper "random matrices and random permutations" by Andrei Okounkov, which is very beautifully written. I just have several technical questions about some of the computations:

  1. in section 2.1.2, why is it clear that only the eigenvalues near the edges of the Wigner's semicircle contribute to the asymptotics of (2.1)? In the same spirit, on page 8, section 2.1.3, the author claims that it is easy to see that by taking a suitable linear combination we can single out hte contribution of only the maximal eigenvalues in formula (2.1). I don't quite see how a winner takes all argument can be applied.
Bounty Started worth 50 reputation by John Jiang
Source Link
John Jiang
John Jiang
  • 4.5k
  • 25
  • 47

edge distribution of random young diagram

I am reading the paper "random matrices and random permutations" by Andrei Okounkov, which is very beautifully written. I just have several technical questions about some of the computations:

  1. in section 2.1.2, why is it clear that only the eigenvalues near the edges of the Wigner's semicircle contribute to the asymptotics of (2.1)? In the same spirit, on page 8, section 2.1.3, the author claims that it is easy to see that by taking a suitable linear combination we can single out hte contribution of only the maximal eigenvalues in formula (2.1). I don't quite see how a winner takes all argument can be applied.