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تسجيل مستخدم جديدOn eigenvalues of the Brownian sheet matrix
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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 $left{L_{d}(s,t), (s,t)in[0,S]times [0,T]right}_{dinmathbb N}$ of empirical spectral measures of the rescaled matrices is tight on $C([0,S]times [0,T], mathcal P(mathbb R))$ and hence is convergent as $d$ goes to infinity by Wigners semicircle law. We also obtain PDEs which are satisfied by the high-dimensional limiting measure.
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