The barycenter conjecture for one-dimensional free Gibbs measures
Let f:R→\textbackslashRf:\mathbb{R}\rightarrow\textbackslash \mathbb{R}f:R→\textbackslashR be continuous and satisfy the assumptions denoted by (gibbs)(\mathrm{gibbs})(gibbs). For λ\textbackslashinR\lambda\textbackslash in\mathbb{R}λ\textbackslashinR, let the fr…