probability-positive-definiteness-gGUE-semi-classical-Laguerre-polynomials-Simm-2017.pdf (232.39 kB)
On the probability of positive-definiteness in the gGUE via semi-classical Laguerre polynomials
journal contribution
posted on 2023-06-09, 13:20 authored by Alfredo Deano, Nicholas SimmNicholas SimmIn this paper, we compute the probability that an N x N matrix from the generalized Gaussian Unitary Ensemble (gGUE) is positive definite, extending a previous result of Dean and Majumdar (2008). For this purpose, we work out the large degree asymptotics of semi-classical Laguerre polynomials and their recurrence coefficients, using the steepest descent analysis of the corresponding Riemann–Hilbert problem.
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Publication status
- Published
File Version
- Accepted version
Journal
Journal of Approximation TheoryISSN
0021-9045Publisher
ElsevierExternal DOI
Volume
220Page range
44-59Department affiliated with
- Mathematics Publications
Research groups affiliated with
- Probability and Statistics Research Group Publications
- Mathematical Physics Group Publications
Full text available
- Yes
Peer reviewed?
- Yes
Legacy Posted Date
2018-06-12First Open Access (FOA) Date
2018-06-12First Compliant Deposit (FCD) Date
2018-06-12Usage metrics
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