Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the distribution of the length of the second row of a Young diagram
  under Plancherel measure   We investigate the probability distribution of the length of the second row
of a Young diagram of size $N$ equipped with Plancherel measure. We obtain an
expression for the generating function of the distribution in terms of a
derivative of an associated Fredholm determinant, which can then be used to
show that as $N\to\infty$ the distribution converges to the Tracy-Widom
distribution [TW] for the second largest eigenvalue of a random GUE matrix.
This paper is a sequel to [BDJ], where we showed that as $N\to\infty$ the
distribution of the length of the first row of a Young diagram, or
equivalently, the length of the longest increasing subsequence of a random
permutation, converges to the Tracy-Widom distribution [TW] for the largest
eigenvalue of a random GUE matrix.

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The categories of this paper are: plasm-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: chem-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: dg-ga
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The categories of this paper are: supr-con
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The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
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The categories of this paper are: hep-th
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The categories of this paper are: eess
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The categories of this paper are: nucl-th
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The categories of this paper are: funct-an
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The categories of this paper are: q-alg
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The categories of this paper are: cs
16
The categories of this paper are: stat
4
The categories of this paper are: cond-mat