Some aspects of large time behavior of the heat kernel: an overview with   perspectives
  We discuss a variety of developments in the study of large time behavior of the positive minimal heat kernel of a time independent (not necessarily symmetric) second-order parabolic operator defined on a domain M in $R^d$, or more generally, on a noncompact Riemannian manifold M. Our attention is mainly focused on general results in general settings. 
Yehuda Pinchover
math.AP math.SP