  In this work we design a general method for proving moment inequalities for
polynomials of independent random variables. Our method works for a wide range
of random variables including Gaussian, Boolean, exponential, Poisson and many
others. We apply our method to derive general concentration inequalities for
polynomials of independent random variables. We show that our method implies
concentration inequalities for some previously open problems, e.g. permanent of
a random symmetric matrices. We show that our concentration inequality is
stronger than the well-known concentration inequality due to Kim and Vu. The
main advantage of our method in comparison with the existing ones is a wide
range of random variables we can handle and bounds for previously intractable
regimes of high degree polynomials and small expectations. On the negative side
we show that even for boolean random variables each term in our concentration
inequality is tight.
