  We develop and implement new probabilistic strategy for proving exponential
ergodicity for interacting diffusion processes on unbounded lattice. The
concept of the solution used is rather weak as we construct the process in
infinite dimension as a solution to suitable infinite dimensional martingale
problem. However the techniques allow us to consider cases where the generator
of the particle is subelliptic operator. In addition we prove exponential
convergence in the uniform norm, which appears to be new in this context. As a
model case we present situation, where the operator arises from Heisenberg
group. In the last section we mention some further examples that can be handled
using our methods.
