Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Exact asymptotics of the characteristic polynomial of the symmetric
  Pascal matrix   We have obtained the exact asymptotics of the determinant $\det_{1\leq
r,s\leq L}[\binom{r+s-2}{r-1}+\exp(i\theta)\delta_{r,s}]$. Inverse symbolic
computing methods were used to obtain exact analytical expressions for all
terms up to relative order $L^{-14}$ to the leading term. This determinant is
known to give weighted enumerations of cyclically symmetric plane partitions,
weighted enumerations of certain families of vicious walkers and it has been
conjectured to be proportional to the one point function of the O$(1)$ loop
model on a cylinder of circumference $L$. We apply our result to the loop model
and give exact expressions for the asymptotics of the average of the number of
loops surrounding a point and the fluctuation in this number. For the related
bond percolation model, we give exact expressions for the asymptotics of the
probability that a point is on a cluster that wraps around a cylinder of even
circumference and the probability that a point is on a cluster spanning a
cylinder of odd circumference.

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The categories of this paper are: hep-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: physics
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The categories of this paper are: adap-org
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The categories of this paper are: q-bio
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The categories of this paper are: chem-ph
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The categories of this paper are: astro-ph
1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
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The categories of this paper are: quant-ph
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The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
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The categories of this paper are: supr-con
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The categories of this paper are: hep-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: stat