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We show decay estimates for the propagator of the discrete Schr\"odinger andKlein-Gordon equations in the form $\norm{U(t)f}{l^\infty}\leq C(1+|t|)^{-d/3}\norm{f}{l^1}$. This implies a corresponding (restricted) set ofStrichartz estimates. Applications of the latter include the existence ofexcitation thresholds for certain regimes of the parameters and the decay ofsmall initial data for relevant $l^p$ norms. The analytical decay estimates arecorroborated with numerical results.Comment: 13 pages, 4 figure

Asymptotic behaviour of small solutions for the discrete nonlinear Schrödinger and Klein–Gordon equations