Long time behavior of heat kernels of operators with unbounded drift terms

Given a second-order elliptic operator on R d , with bounded diffusion coefficients and unbounded drift, which is the generator of a strongly continuous semigroup on L 2 ( R d ) represented by an integral, we study the time behavior of the integral kernel and prove estimates on its decay at infinity. If the diffusion coefficients are symmetric, a local lower estimate is also proved.