We prove Landis-type uniqueness results for both the semidiscrete heat and the stationary discrete Schrödinger equations. To establish a nomenclature, we refer to Landis-type results when we are interested in the maximum vanishing rate of solutions to equations with potentials. The results are obtained through quantitative estimates within a spatial lattice which manifest an interpolation phenomenon between continuum and discrete scales. In the case of the elliptic equation, these quantitative estimates exhibit a rate decay which, in the range close to continuum, coincides with the same exponent as in the classical results of the Landis conjecture in the Euclidean setting.
Joint work with Aingeru Fern'andez-Bertolin and Diana Stan.