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We study models of continuous-time, symmetric, $\Z^{d}$-valued random walksin random environments, driven by a field of i.i.d. random nearest-neighborconductances $\omega_{xy}\in[0,1]$ with a power law with an exponent $\gamma$near 0. We are interested in estimating the quenched decay of the returnprobability $P_\omega^{t}(0,0)$, as $t$ tends to $+\infty$. We show that for$\gamma> \frac{d}{2}$, the standard bound turns out to be of the correctlogarithmic order. As an expected concequence, the same result holds for thediscrete-time case.

Standard Spectral Dimension for the Polynomial Lower Tail Random Conductances model