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On the Tracy-Widomβ Distribution for β=6
Symmetry, Integrability and Geometry: Methods and Applications
We study the Tracy-Widom distribution function for Dyson's β-ensemble with β = 6. The starting point of our analysis is the recent work of I. Rumanov where he produces a Lax-pair representation for the Bloemendal-Virág equation. The latter is a linear PDE which describes the Tracy-Widom functions corresponding to general values of β. Using his Lax pair, Rumanov derives an explicit formula for the Tracy-Widom β=6 function in terms of the second Painlevé transcendent and the solution of andoi:10.3842/sigma.2016.105 fatcat:3htguzf33zdezeawbq4jvckusm