Approximation of Beta-Jacobi Ensembles by Beta-Laguerre Ensembles.

Ma, Yutao; Shen, Xinmei

Consider beta-Laguerre ensembles μ with parameters m, a1 and beta-Jacobi ensembles γ with parameters m, a1, a2. With the help of tridiagonal models of beta ensembles, we are able to prove that lim a 2 → ∞ d (L (2 a λ) , L (μ)) = 0 if a 1 m = o (a 2) and lim _ a 2 → ∞ d (L (2 a λ) , L (μ)) > 0 if lim a 2 → ∞ a 1 m a 2 = σ > 0 , by contrast, where a ≔ a1 a2 and d is total variation distance or Kullback—Leibler divergence. This result improves the approximation in [9].

MATHEMATICS; DIVERGENCE (Meteorology); DYNAMIC meteorology; TRIDIAGONAL Solutions (Company); ATMOSPHERIC waves

Frontiers of Mathematics, 2023, Vol 18, Issue 1, p225

2731-8648

Academic Journal

10.1007/s11464-020-0018-y