论文标题
随机量子图
Random quantum graphs
论文作者
论文摘要
We prove a number of results to the effect that generic quantum graphs (defined via operator systems as in the work of Duan-Severini-Winter / Weaver) have few symmetries: for a Zariski-dense open set of tuples $(X_1,\cdots,X_d)$ of traceless self-adjoint operators in the $n\times n$ matrix algebra the corresponding operator system has trivial自动形态组，参数可能最大的范围：$ 2 \ le d \ le n^2-3 $。此外，自动形态组在较大的参数范围内通常是Abelian $ 1 \ le d \ le n^2-2 $。然后，这意味着对于这些参数，相应的随机Quantum-graph模型构建在$ x_i $'s的Gue合奏（模仿Erdős-rényi$ g（n，p）$模型）几乎肯定地肯定。
We prove a number of results to the effect that generic quantum graphs (defined via operator systems as in the work of Duan-Severini-Winter / Weaver) have few symmetries: for a Zariski-dense open set of tuples $(X_1,\cdots,X_d)$ of traceless self-adjoint operators in the $n\times n$ matrix algebra the corresponding operator system has trivial automorphism group, in the largest possible range for the parameters: $2\le d\le n^2-3$. Moreover, the automorphism group is generically abelian in the larger parameter range $1\le d\le n^2-2$. This then implies that for those respective parameters the corresponding random-quantum-graph model built on the GUE ensembles of $X_i$'s (mimicking the Erdős-Rényi $G(n,p)$ model) has trivial/abelian automorphism group almost surely.
