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Freezing limits for Calogero–Moser–Sutherland particle models
starts in 0 ∈ 𝐶𝐴𝑁 , then 𝑋𝑡,𝑘 has the density
𝑐𝐴 𝑘
𝑡𝛾+𝑁∕2 𝑒−‖𝑦‖2∕(2𝑡) ⋅ 𝑤𝑘(𝑦) 𝑑𝑦 (9)
on 𝐶𝐴𝑁 for 𝑡 > 0. In particular, for 𝑘 = 1∕2, 1, 2, the distributions of the ordered eigenvalues [...] dimensions 𝑑 = 1, 2, 4 for 𝑘 = 𝑑∕2 = 1∕2, 1, 2. Moreover, for general 𝑘 > 0, the distributions (9) belong to the 𝛽-Hermite ensembles that are
the eigenvalue distributions of well-known tridiagonal [...] Remark 4 for more details. We next turn to the limit 𝑘 → ∞ in the first approach according to [4, 5, 7-9, 35, 43]. If we start
in 0 ∈ 𝐶𝐴𝑁 , we write the densities of 𝑋𝑡,𝑘∕ √ 𝑡𝑘 as
𝑐𝑜𝑛𝑠𝑡.(𝑘) ⋅ …