Abstract
Double-scaling limits of Toeplitz determinants Dn(ft) generated by a set of functions ft ∈ L1 are discussed as both n → ∞ and t → 0 simultaneously, which is currently of great importance in mathematics and in physics. The main focus is on the cases where the number of Fisher–Hartwig singularities changes as t → 0. All the results on double-scaling limits are discussed in the context of applications in random matrix theory and in mathematical physics.
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