  In this paper we consider the reconstruction problem on the tree for the
hardcore model. We determine new bounds for the non-reconstruction regime on
the k-regular tree showing non-reconstruction when lambda < (ln
2-o(1))ln^2(k)/(2 lnln(k)) improving the previous best bound of lambda < e-1.
This is almost tight as reconstruction is known to hold when lambda>
(e+o(1))ln^2(k). We discuss the relationship for finding large independent sets
in sparse random graphs and to the mixing time of Markov chains for sampling
independent sets on trees.
