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We prove a quenched local central limit theorem for continuous-time randomwalks in $\mathbb Z^d, d\ge 2$, in a uniformly-elliptic time-dependent balancedrandom environment which is ergodic under space-time shifts. We also obtainGaussian upper and lower bounds for quenched and (positive and negative) momentestimates of the transition probabilities and asymptotics of the discrete Greenfunction.

Quenched local central limit theorem for random walks in a time-dependent balanced random environment