  This paper studies the deflation algorithm when applied to estimate a
low-rank symmetric spike contained in a large tensor corrupted by additive
Gaussian noise. Specifically, we provide a precise characterization of the
large-dimensional performance of deflation in terms of the alignments of the
vectors obtained by successive rank-1 approximation and of their estimated
weights, assuming non-trivial (fixed) correlations among spike components. Our
analysis allows an understanding of the deflation mechanism in the presence of
noise and can be exploited for designing more efficient signal estimation
methods.
