Unconditional arithmetic circuit lower bounds for permanent/determinant In this http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.12.1090&amp;rep=rep1&amp;type=pdf an unconditional lower bound (provided constants used are bounded by absolute value smaller than $1$) of $\Omega(n^2\log n)$ for size of arithmetic circuits computing $n\times n$ Matrix Multiplication is given.

What is the best unconditional lower bound for size of arithmetic circuits computing $n\times n$ Matrix Determinant and Permanent along similar lines?
Kalorkoti gave an $\Omega(n^3)$ lower bound on arithmetic formulas for the determinant and permanent. As far as I know, nothing is known for unrestricted circuits.