论文标题
Wigner矩阵多项式产生的渐近freenestotic freeness
Asymptotic freeness through unitaries generated by polynomials of Wigner matrices
论文作者
论文摘要
我们研究确定性矩阵和独立WIGNER矩阵中自动辅助多项式评估的功能产物；我们计算此类产品的确定性近似值并控制波动。我们专注于最大程度地减少这些功能的平滑度的假设，同时优化$ n $（矩阵的大小）的错误项。作为一个应用程序，我们基于这样的想法，即与Wigner矩阵相关的长期Heisenberg进化会产生渐近的Freeness，如$ [9] $中的首次显示。更确切地说，$ p $是自我偶像非交易性多项式和$ y^n $ a $ d $ - 独立的Wigner矩阵的负数，我们证明与操作员$ p（y^n）$产量相关的量子进化是大时的差异。
We study products of functions evaluated at self-adjoint polynomials in deterministic matrices and independent Wigner matrices; we compute the deterministic approximations of such products and control the fluctuations. We focus on minimizing the assumption of smoothness on those functions while optimizing the error term with respect to $N$, the size of the matrices. As an application, we build on the idea that the long-time Heisenberg evolution associated to Wigner matrices generates asymptotic freeness as first shown in $[9]$. More precisely given $P$ a self-adjoint non-commutative polynomial and $Y^N$ a $d$-tuple of independent Wigner matrices, we prove that the quantum evolution associated to the operator $P(Y^N)$ yields asymptotic freeness for large times.
