In the thermal hyperbolic Calogero fluid, the Lax-matrix eigenvalue density is computed numerically and matches a generalized log-gas, with weak boundary-condition dependence in the thermodynamic limit.
Cao, Classical integrable systems, In Soliton Theory and Its Applications, Springer, 152 (1990) https://link.springer.com/chapter/10.1007/978-3-662-03102-5_4
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Lax random matrices from Calogero systems
In the thermal hyperbolic Calogero fluid, the Lax-matrix eigenvalue density is computed numerically and matches a generalized log-gas, with weak boundary-condition dependence in the thermodynamic limit.