Tail conditional expectations refer to the expected values of random variables conditioning on some tail events and are closely related to various coherent risk measures. In the univariate case, the tail conditional expectation is asymptotically proportional to the value-at-risk, a popular risk measure. The focus of this paper is on asymptotic relations between the multivariate tail conditional...

We prove the asymptotic of logarithmic Bergman kernel. And as an application, we calculate conditional expectation density zeros Gaussian random sections powers a positive line bundle that vanish along fixed smooth subvariety.