Toeplitz and Wiener-Hopf determinants with piecewise continuous symbols

Asymptotics of a Fredholm Determinant Corresponding to the First Bulk Critical Universality Class in Random Matrix Models

“…[2,4,44,45,50] and [18] for more on the history of the question) The latter constant was obtained by A. Budylin and V. Buslaev as a corollary to their main result in [4], namely the asymptotics of the resolvent of the kernel γK sin (λ, µ). Formula (1.17) also follows from the general theorem of E. Basor and H. Widom concerning the determinants of Toeplitz integral operators with piecewise continuous symbols [3].…”

Powers of large random unitary matrices and Toeplitz determinants

“…Such results have often been investigated before; see for example [2,14]. However, all the results known thus far use the fact that H(a)H(b) is of trace class.…”

“…First we will show that the Hilbert-Schmidt norm of T n (b − 1) tends to 0 as n → ∞; hence the regularized determinant tends to 1. Second, we show that Tr T n (b − 1) − C (2) tends to 0 as n → ∞. Then (1.14) follows by (3.7) and (3.8).…”

“…The results of this computation can be used for proving (1.12). Hence, in the remaining proof of (1.12) we can restrict ourselves to only those parts that come in by interaction of g (1) and g (2) . In our opinion, it helps to get a better understanding of the problem.…”

A Strong Central Limit Theorem for a Class of Random Surfaces

“…The inequality (1.11) for x lying along lattice lines follows from earlier work [1] on Toeplitz determinants for piecewise smooth symbols. These results allow for a larger range of δ in (1.11) than [11] does.…”