Entries of the inverses of large positive definite Toeplitz matrices. (English) Zbl 07614111
Summary: This is an expository paper embarking on the asymptotic behavior of the entries of the inverses of positive definite symmetric Toeplitz matrices as the matrix dimension goes to infinity. We consider the behavior of the entries in neighborhoods of the four corners as well as the density of the distribution of the entries over all of the inverse matrix.
MSC:
| 15B05 | Toeplitz, Cauchy, and related matrices |
| 47B35 | Toeplitz operators, Hankel operators, Wiener-Hopf operators |
| 34B27 | Green’s functions for ordinary differential equations |
| 60G50 | Sums of independent random variables; random walks |
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