On eigenvalues of the Brownian sheet matrix
arxiv(2023)
摘要
We derive a system of stochastic partial differential equations satisfied by the eigenvalues of the symmetric matrix whose entries are the Brownian sheets. We prove that the sequence Ld(s,t),(s,t)∈[0,S]×[0,T]d∈N of empirical spectral measures of the rescaled matrices is tight on C([0,S]×[0,T],P(R)) and hence is convergent as d goes to infinity by Wigner’s semicircle law. We also obtain PDEs which are satisfied by the high-dimensional limiting measure.
更多查看译文
关键词
eigenvalues
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络
Chat Paper
正在生成论文摘要