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It is shown that \\[ \\ln \\mathbb{P}\\left( \\sum_{k\\in\\mathbb{Z}} d_k^2 U_k^2 \\leq \\varepsilon^2\\right) \\sim - M \\varepsilon^{-\\frac{2}{2p-1}}, \\qquad \\textrm{ as } \\varepsilon\\to 0, \\] whenever \\[ d_k\\sim d_{\\pm} |k|^{-p}\\quad \\textrm{for some } p>\\frac{1}{2} \\, , \\quad k\\to \\pm\\infty, \\] using the arguments based on the spectral theory of pseudo-differential operators by M. 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