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- W4300672922 abstract "We review some occurrences of Painlev'e 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 Painlev'e equation is zero, and the boundary condition is that of the Hasting-MacLeod solution. As well as expressions involving the Painlev'e transcendent itself, one encounters the sigma form of the Painlev'e II equation, and Lax pair equations in which the Painlev'e transcendent occurs as coefficients. We then consider settings which give rise to general $alpha$ Painlev'e 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.
- W4300672922 created "2022-10-04" @default.
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- W4300672922 date "2012-10-11" @default.
- W4300672922 modified "2023-10-18" @default.
- W4300672922 title "Painleve II in random matrix theory and related fields" @default.
- W4300672922 doi "https://doi.org/10.48550/arxiv.1210.3381" @default.
- W4300672922 hasPublicationYear "2012" @default.
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