Abstract
AbstractLet $$(\sigma _N^{(i)})_{i \in I}$$
(
σ
N
(
i
)
)
i
∈
I
be a family of symmetric permutations of the entries of a Wigner matrix $${\mathbf {W}}_N$$
W
N
. We characterize the limiting traffic distribution of the corresponding family of dependent Wigner matrices $$({\mathbf {W}}_N^{\sigma _N^{(i)}})_{i \in I}$$
(
W
N
σ
N
(
i
)
)
i
∈
I
in terms of the geometry of the permutations. We also consider the analogous problem for the limiting joint distribution of $$({\mathbf {W}}_N^{\sigma _N^{(i)}})_{i \in I}$$
(
W
N
σ
N
(
i
)
)
i
∈
I
. In particular, we obtain a description in terms of semicircular families with general covariance structures. As a special case, we derive necessary and sufficient conditions for traffic independence as well as sufficient conditions for free independence.
Publisher
Springer Science and Business Media LLC
Subject
Statistics, Probability and Uncertainty,Statistics and Probability,Analysis
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