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Browsing by Author "Basor, Estelle"
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Item Asymptotics of bordered Toeplitz determinants and next-to-diagonal Ising correlations(arXiv, 2021) Basor, Estelle; Ehrhardt, Torsten; Gharakhloo, Roozbeh; Its, Alexander; Li, Yuqi; Mathematical Sciences, School of ScienceWe prove the analogue of the strong Szeg{\H o} limit theorem for a large class of bordered Toeplitz determinants. In particular, by applying our results to the formula of Au-Yang and Perk \cite{YP} for the next-to-diagonal correlations ⟨σ0,0σN−1,N⟩ in the anisotropic square lattice Ising model, we rigorously justify that the next-to-diagonal long-range order is the same as the diagonal and horizontal ones in the low temperature regime. The anisotropy-dependence of the subleading term in the asymptotics of the next-to-diagonal correlations is also established. We use Riemann-Hilbert and operator theory techniques, independently and in parallel, to prove these results.Item Exact Solution of the Classical Dimer Model on a Triangular Lattice: Monomer-Monomer Correlations(Springer, 2017-12) Basor, Estelle; Bleher, Pavel; Mathematical Sciences, School of ScienceWe obtain an asymptotic formula, as n→∞, for the monomer–monomer correlation function K2(n) in the classical dimer model on a triangular lattice, with the horizontal and vertical weights wh=wv=1 and the diagonal weight wd=t>0, between two monomers at vertices q and r that are n spaces apart in adjacent rows. We find that tc=12 is a critical value of t. We prove that in the subcritical case, 0Item A representation of joint moments of CUE characteristic polynomials in terms of Painlevé functions(IOP, 2019-10) Basor, Estelle; Bleher, Pavel; Buckingham, Robert; Grava, Tamara; Its, Alexander; Its, Elizabeth; Keating, Jonathan P.; Mathematical Sciences, School of ScienceWe establish a representation of the joint moments of the characteristic polynomial of a CUE random matrix and its derivative in terms of a solution of the -Painlevé V equation. The derivation involves the analysis of a formula for the joint moments in terms of a determinant of generalised Laguerre polynomials using the Riemann–Hilbert method. We use this connection with the -Painlevé V equation to derive explicit formulae for the joint moments and to show that in the large-matrix limit the joint moments are related to a solution of the -Painlevé III equation. Using the conformal block expansion of the -functions associated with the -Painlevé V and the -Painlevé III equations leads to general conjectures for the joint moments.