非线性随机矩阵统计、对称函数与超行列式
Nonlinear Random Matrix Statistics, symmetric functions and hyperdeterminants
摘要：
本文研究了Dyson三对称类$β=1,2,4$的不变随机矩阵模型特征值的非线性统计（即不变量的统计）。找到了$β=2$的超行列式通式。对于特定的情况和所有的$β$ s，更计算效率的结果，得到的基础上对称函数的扩展。作为应用，我们考虑了混沌腔中量子输运的情况，推广了[D. V. Savin，H.- J. Sommers和W. Wieczorek，{ \it Phys. Rev. B} { \bf 77}，125332（2008）]。
英文摘要：
Nonlinear statistics (i.e. statistics of permanents) on the eigenvalues of invariant random matrix models are considered for the three Dyson's symmetry classes $β=1,2,4$. General formulas in terms of hyperdeterminants are found for $β=2$. For specific cases and all $β$s, more computationally efficient results are obtained, based on symmetric functions expansions. As an application, we consider the case of quantum transport in chaotic cavities extending results from [D.V. Savin, H.-J. Sommers and W. Wieczorek, {\it Phys. Rev. B} {\bf 77}, 125332 (2008)].
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