Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $\beta$-Nonintersecting Poisson Random Walks: Law of Large Numbers and
  Central Limit Theorems   We study the $\beta$ analogue of the nonintersecting Poisson random walks. We
derive a stochastic differential equation of the Stieltjes transform of the
empirical measure process, which can be viewed as a dynamical version of the
Nekrasov's equation in [7, Section 4]. We find that the empirical measure
process converges weakly in the space of c\'adl\'ag measure-valued processes to
a deterministic process, characterized by the quantized free convolution, as
introduced in [11]. For suitable initial data, we prove that the rescaled
empirical measure process converges weakly in the space of distributions acting
on analytic test functions to a Gaussian process. The means and the covariances
are universal, and coincide with those of $\beta$-Dyson Brownian motions with
the initial data constructed by the Markov-Krein correspondence. Especially,
the covariance structure can be described in terms of the Gaussian Free Field.
Our proof relies on integrable features of the generators of the
$\beta$-nonintersecting Poisson random walks, the method of characteristics,
and a coupling technique for Poisson random walks.

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The categories of this paper are: nlin
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The categories of this paper are: quant-ph
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The categories of this paper are: gr-qc
3
The categories of this paper are: physics
14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
11
The categories of this paper are: hep-lat
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The categories of this paper are: funct-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: alg-geom
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The categories of this paper are: supr-con
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The categories of this paper are: eess
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The categories of this paper are: econ
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The categories of this paper are: patt-sol
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The categories of this paper are: nucl-th