Guangqian Zhao

Gaussian Exterior Dilation and Schatten Classes of L\'evy Area

We study the skew-adjoint Hilbert--Schmidt operator obtained by evaluating a fixed Hilbert two-form on a centered Gaussian linear map whose covariance is the inner product on its domain multiplied by a fixed nonnegative trace-class operator. We compute the expected regularized determinant of the resulting random operat...

INFINITE-DIMENSIONAL L´EVY AREA: SHARP OPERATOR-IDEAL REGULARITY AND ANISOTROPIC IT ˆO GEOMETRY

INFINITE-DIMENSIONAL L´EVY AREA: PROBABILITY-SELECTED CRITICAL GEOMETRY AND SHARP SPECTRAL SELECTION