On lacunary Toeplitz determinants

By using Riemann-Hilbert problem based techniques, we obtain the asymptotic expansion of lacunary Toeplitz determinants det(N)[cl(a)-m(b) [f]] generated by holomorphic symbols, where l(a) = a (resp. m(b) = b) except for a finite subset of indices a = h(1),..., h(n) (resp. b = t(1),..., t(r)). In addition to the usual Szego asymptotics, our answer involves a determinant of size n + r.