Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Random Matrices, the Ulam Problem, Directed Polymers & Growth Models,
  and Sequence Matching   In these lecture notes I will give a pedagogical introduction to some common
aspects of 4 different problems: (i) random matrices (ii) the longest
increasing subsequence problem (also known as the Ulam problem) (iii) directed
polymers in random medium and growth models in (1+1) dimensions and (iv) a
problem on the alignment of a pair of random sequences. Each of these problems
is almost entirely a sub-field by itself and here I will discuss only some
specific aspects of each of them. These 4 problems have been studied almost
independently for the past few decades, but only over the last few years a
common thread was found to link all of them. In particular all of them share
one common limiting probability distribution known as the Tracy-Widom
distribution that describes the asymptotic probability distribution of the
largest eigenvalue of a random matrix. I will mention here, without
mathematical derivation, some of the beautiful results discovered in the past
few years. Then, I will consider two specific models (a) a ballistic deposition
growth model and (b) a model of sequence alignment known as the Bernoulli
matching model and discuss, in some detail, how one derives exactly the
Tracy-Widom law in these models. The emphasis of these lectures would be on how
to map one model to another. Some open problems are discussed at the end.

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The categories of this paper are: nlin
1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
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The categories of this paper are: acc-phys
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The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
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The categories of this paper are: plasm-ph
34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
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The categories of this paper are: q-bio
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The categories of this paper are: adap-org
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The categories of this paper are: hep-ex
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The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: stat