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- W2953022969 abstract "We review some occurrences of Painleve II transcendents in the study of two-dimensional Yang-Mills theory, fluctuation formulas for growth models, and as distribution functions within random matrix theory. We first discuss settings in which the parameter $alpha$ in the Painleve equation is zero, and the boundary condition is that of the Hasting-MacLeod solution. As well as expressions involving the Painleve transcendent itself, one encounters the sigma form of the Painleve II equation, and Lax pair equations in which the Painleve transcendent occurs as coefficients. We then consider settings which give rise to general $alpha$ Painleve II transcendents. In a particular random matrix setting, new results for the corresponding boundary conditions in the cases $alpha = pm 1/2$, 1 and 2 are presented." @default.
- W2953022969 created "2019-06-27" @default.
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- W2953022969 date "2012-10-11" @default.
- W2953022969 modified "2023-09-27" @default.
- W2953022969 title "Painleve II in random matrix theory and related fields" @default.
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