Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Counting independent sets in unbalanced bipartite graphs   We give an FPTAS for approximating the partition function of the hard-core
model for bipartite graphs when there is sufficient imbalance in the degrees or
fugacities between the sides $(L,R)$ of the bipartition. This includes, among
others, the biregular case when $\lambda=1$ (approximating the number of
independent sets of $G$) and $\Delta_R \geq 7\Delta_L \log(\Delta_L)$. Our
approximation algorithm is based on truncating the cluster expansion of a
polymer model partition function that expresses the hard-core partition
function in terms of deviations from independent sets that are empty on one
side of the bipartition. As a consequence of the method, we also prove that the
hard-core model on such graphs exhibits exponential decay of correlations by
utilizing connections between the cluster expansion and joint cumulants.

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The categories of this paper are: comp-gas
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The categories of this paper are: atom-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: adap-org
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The categories of this paper are: chem-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: quant-ph
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The categories of this paper are: stat
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The categories of this paper are: nlin
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The categories of this paper are: alg-geom
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The categories of this paper are: math-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-ex
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The categories of this paper are: econ
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The categories of this paper are: hep-ph
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The categories of this paper are: patt-sol