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Global spectrum fluctuations for Gaussian beta ensembles: a martingale approach. (arXiv:1710.03921v1 [math.PR])
来源于:arXiv
The paper describes the global limiting behavior of Gaussian beta ensembles
where the parameter $\beta$ is allowed to vary with the matrix size $n$. In
particular, we show that as $n \to \infty$ with $n\beta \to \infty$, the
empirical distribution converges weakly to the semicircle distribution, almost
surely. The Gaussian fluctuation around the limit is then derived by a
martingale approach. 查看全文>>