Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nonintersecting Paths, Noncolliding Diffusion Processes and
  Representation Theory   The system of one-dimensional symmetric simple random walks, in which none of
walkers have met others in a given time period, is called the vicious walker
model. It was introduced by Michael Fisher and applications of the model to
various wetting and melting phenomena were described in his Boltzmann medal
lecture. In the present report, we explain interesting connections among
representation theory, probability theory, and random matrix theory using this
simple diffusion particle system. Each vicious walk of $N$ walkers is
represented by an $N$-tuple of nonintersecting lattice paths on the
spatio-temporal plane. There is established a simple bijection between
nonintersecting lattice paths and semistandard Young tableaux. Based on this
bijection and some knowledge of symmetric polynomials called the Schur
functions, we can give a determinantal expression to the partition function of
vicious walks, which is regarded as a special case of the Karlin-McGregor
formula in the probability theory (or the Lindstr\"om-Gessel-Viennot formula in
the enumerative combinatorics). Due to a basic property of Schur function, we
can take the diffusion scaling limit of the vicious walks and define a
noncolliding system of Brownian particles. This diffusion process solves the
stochastic differential equations with the drift terms acting as the repulsive
two-body forces proportional to the inverse of distances between particles, and
thus it is identified with Dyson's Brownian motion model. In other words, the
obtained noncolliding system of Brownian particles is equivalent in
distribution with the eigenvalue process of a Hermitian matrix-valued process.

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The categories of this paper are: eess
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The categories of this paper are: atom-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: adap-org
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The categories of this paper are: comp-gas
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The categories of this paper are: solv-int
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The categories of this paper are: plasm-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: quant-ph
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The categories of this paper are: supr-con
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The categories of this paper are: q-fin
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The categories of this paper are: hep-ph
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The categories of this paper are: physics
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The categories of this paper are: bayes-an