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New critical matrix models and generalized universality

“…This rescaling is the only consistent way to obtain a finite large-N differential equation from eq. (3.3) and it agrees with the rescaling in the pure Freud case obtained in [19,20,21,22] when translating to their conventions. Eq.…”

“…The spectral density for a single nonpolynomial potential V (λ) = |λ| κ has been calculated already in [19,20,21,22]. In order to determine the full density ρ(λ) for the potential eq.…”

“…Imposing the condition 1 = Hgc κ we would obtain a normalized density, reproducing [19,20,22]. By adding the two solutions eqs.…”

“…Single nonpolynomial potentials have been already studied in [19,20,21,22]. They have been shown to fall into the microscopic universality class of the sine kernel in the bulk and at the origin of the spectrum.…”

An Update on Local Universality Limits for Correlation Functions Generated by Unitary Ensembles

“…Using direct substitution into the Christoffel-Darboux formula, this must lead to universality both in the bulk and at the soft-edge, although this was not stated there. Another powerful paper that implies universality results, but which are not explicitly stated, is that of Kriecherbauer and McLaughlin [35], for exp(−|x| α ), all α > 0. Of course, there was a lot of earlier work for such asymptotics, that also implies universality in the bulk, at least, for various exponential weights.…”