Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stein's method for dependent random variables occurring in Statistical
  Mechanics   We obtain rates of convergence in limit theorems of partial sums $S_n$ for
certain sequences of dependent, identically distributed random variables, which
arise naturally in statistical mechanics, in particular, in the context of the
Curie-Weiss models. Under appropriate assumptions there exists a real number
$\alpha$, a positive real number $\mu$, and a positive integer $k$ such that
$(S_n- n \alpha)/n^{1 - 1/2k}$ converges weakly to a random variable with
density proportional to $\exp(-\mu |x|^{2k} /(2k)!)$. We develop Stein's method
for exchangeable pairs for a rich class of distributional approximations
including the Gaussian distributions as well as the non-Gaussian limit
distributions with density proportional to $\exp(-\mu |x|^{2k} /(2k)!)$. Our
results include the optimal Berry-Esseen rate in the Central Limit Theorem for
the total magnetization in the classical Curie-Weiss model, for high
temperatures as well as at the critical temperature $\beta_c=1$, where the
Central Limit Theorem fails. Moreover, we analyze Berry-Esseen bounds as the
temperature $1/ \beta_n$ converges to one and obtain a threshold for the speed
of this convergence. Single spin distributions satisfying the
Griffiths-Hurst-Sherman (GHS) inequality like models of liquid helium or
continuous Curie-Weiss models are considered.

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The categories of this paper are: atom-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: ao-sci
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-alg
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: math-ph
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The categories of this paper are: adap-org
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The categories of this paper are: solv-int
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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: mtrl-th
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The categories of this paper are: astro-ph
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The categories of this paper are: quant-ph