论文标题
在双重图上的因子模型的自由能密度上
On the free energy density of factor models on biregular graphs
论文作者
论文摘要
令$ h（0），h（1），\ dots，h（k）$为对称凹面序列。对于$（d，k）$ - 双重因子图$ g $和$ x \ in \ {0,1 \}^v $，我们定义了hamiltonian \ [h_g（x）= \ sum_ {f \ in f} $ f $是因子节点的集合。我们证明，如果$（g_n）$是$（d，k）$ - 双重因子图的大周长序列，则$ g_n $的自由能密度收敛。限制自由能密度是由伯特（Bethe-Approximation）给出的。
Let $h(0),h(1),\dots,h(k)$ be a symmetric concave sequence. For a $(d,k)$-biregular factor graph $G$ and $x\in \{0,1\}^V$, we define the Hamiltonian \[H_G(x)=\sum_{f\in F} h\left(\sum_{v\in \partial f} x_v\right),\] where $V$ is the set of variable nodes, $F$ is the set of factor nodes. We prove that if $(G_n)$ is a large girth sequence of $(d,k)$-biregular factor graphs, then the free energy density of $G_n$ converges. The limiting free energy density is given by the Bethe-approximation.
