  A solution to the sign problem is the so-called "Lefschetz thimble approach"
where the domain of integration for field variables in the path integral is
deformed from the real axis to a sub-manifold in the complex space. For
properly chosen sub-manifolds ("thimbles") the sign problem disappears or is
drastically alleviated. The parametrization of the thimble by real coordinates
require the calculation of a jacobian with a computational cost of order
O(V^3), where V is proportional to the spacetime volume. In this note we
propose two estimators for this jacobian with a computational cost of order
O(V). We discuss analytically the regimes where we expect the estimator to work
and show numerical examples in two different models.
