论文标题
$ s _ {\ infty} $的星级发电机的中心限制定理，与无可透性CCR-Gue矩阵有关
A central limit theorem for star-generators of $S_{\infty}$, which relates to traceless CCR-GUE matrices
论文作者
论文摘要
我们证明了$ s _ {\ infty} $的星级生成剂的顺序，其中期望功能由$ s _ {\ infty} $的字符提供，并具有权重$（w_1，\ ldots，w_d，w_d，w_d，0,0,0,0,0, \ ldots）$。限制定律被证明是“无可纹身的CCR-GUE”矩阵的定律，这是一个无可划痕的类似物，其中off-diagonal条目$ g_ {i，j} $满足换向关系$ g_ {i，j} g_} g_} g_ {特殊情况$ w_1 = \ cdots = w_d = 1/d $产生了真正的无可透性Gue矩阵的定律，我们从2021年开始检索了Köstler和Nica的结果，从而从1995年开始扩大了Biane的结果。
We prove a limit theorem concerning the sequence of star-generators of $S_{\infty}$, where the expectation functional is provided by a character of $S_{\infty}$ with weights $(w_1, \ldots , w_d, 0,0, \ldots )$ in the Thoma classification. The limit law turns out to be the law of a "traceless CCR-GUE" matrix, an analogue of the traceless GUE where the off-diagonal entries $g_{i,j}$ satisfy the commutation relation $g_{i,j}g_{j,i} = g_{j,i}g_{i,j} + (w_j - w_i)$. The special case $w_1 = \cdots = w_d = 1/d$ yields the law of a bona fide traceless GUE matrix, and we retrieve a result of Köstler and Nica from 2021, which in turn extended a result of Biane from 1995.
