Complex zeros of real ergodic eigenfunctions

We determine the limit distribution (as λ→∞) of complex zeros for holomorphic continuations φ_λ ^? to Grauert tubes of real eigenfunctions of the Laplacian on a real analytic compact Riemannian manifold (M,g) with ergodic geodesic flow. If ({phi_{j_{k}}}) is an ergodic sequence of eigenfunctions, we prove the weak limit formula (frac{1}{lambda_j}[Z_{phi_{j_k}}^{mathbb{C}}] to frac{i}{pi} partialbar{partial} |xi|_g), where ([Z_{phi_{j_k}^{mathbb{C}}}]) is the current of integration over the complex zeros and where (overline{partial}) is with respect to the adapted complex structure of Lempert-Szöke and Guillemin-Stenzel.