Eigenvalue distributions of high-dimensional matrix processes driven by fractional Brownian motion
Abstract
In this article, we study high-dimensional behavior of empirical spectral distributions \LN(t), t∈[0,T]\ for a class of N× N symmetric/Hermitian random matrices, whose entries are generated from the solution of stochastic differential equation driven by fractional Brownian motion with Hurst parameter H ∈(1/2,1). For Wigner-type matrices, we obtain almost sure relative compactness of \LN(t), t∈[0,T]\N∈ N in C([0,T], P( R)) following the approach in Anderson2010; for Wishart-type matrices, we obtain tightness of \LN(t), t∈[0,T]\N∈ N on C([0,T], P( R)) by tightness criterions provided in Appendix subset:tightness argument. The limit of \LN(t), t∈[0,T]\ as N ∞ is also characterised.
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