论文标题
Quasirandom组的Cayley图的量子独特的牙
Quantum Unique Ergodicity for Cayley graphs of quasirandom groups
论文作者
论文摘要
有限的$ g $称为$ c $ - quasirandom（由gowers），如果所有非平淡无奇的$ g $的不平淡无奇的复杂表示形式至少具有$ c $。对于任何单位$ \ ell^{2} $在有限组上的功能，我们将函数的绝对值平方给定的组上的量子概率度量相关联。我们表明，如果一组是高度的quasirandom，那么该组的任何cayley图都具有邻接运算符的正常本质，以使特征函数的量子概率度量与不太小的量子集的量子量相近。
A finite group $G$ is called $C$-quasirandom (by Gowers) if all non-trivial irreducible complex representations of $G$ have dimension at least $C$. For any unit $\ell^{2}$ function on a finite group we associate the quantum probability measure on the group given by the absolute value squared of the function. We show that if a group is highly quasirandom, in the above sense, then any Cayley graph of this group has an orthonormal eigenbasis of the adjacency operator such that the quantum probability measures of the eigenfunctions put close to the correct proportion of their mass on subsets of the group that are not too small.
