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math-ph2016★ 13 cited
On the probability of positive-definiteness in the gGUE via semi-classical Laguerre polynomials
Alfredo Deaño, Nick Simm
In this paper, we compute the probability that an matrix from the generalised Gaussian Unitary Ensemble (gGUE) is positive definite, extending a previous result of Dea…
math-ph2016★ 15 cited
Topological Expansion in the Complex Cubic Log-Gas Model. One-Cut Case
Pavel M. Bleher, Alfredo Deaño, Maxim Yattselev
We prove the topological expansion for the cubic log-gas partition function \[ Z_N(t)= \int_Γ\cdots\int_Γ\prod_{1\leq j<k\leq N}(z_j-z_k)^2 \prod_{k=1}^Ne^{-N\left(-\frac{z^3}{3}+t…