2016/11/17 by Racz, Miklos Z., Richey, Jacob · 1 citation
#FOS: Mathematics #Probability (math.PR) #Statistics Theory (math.ST)
paper · doi:10.48550/arxiv.1611.05838
It is well known that an n × n Wishart matrix with d degrees of freedom is close to the appropriately centered and scaled Gaussian Orthogonal Ensemble (GOE) if d is large enough. Recent work of Bubeck, Ding, Eldan, and Racz, and independently Jiang and Li, shows that the transition happens when d = Θ( n3 ). Here we consider this critical window and explicitly compute the total variation distance between the Wishart and GOE matrices when d / n3 → c ∈ (0, ∞). This shows, in particular, that the phase transition from Wishart to GOE is smooth.