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We consider the dynamics of lattice random walks with resetting. The walkermoving randomly on a lattice of arbitrary dimensions resets at every time stepto a given site with a constant probability $r$. We construct a discreterenewal equation and present closed-form expressions for different quantitiesof the resetting dynamics in terms of the underlying reset-free propagator orGreen's function. We apply our formalism to the biased random walk dynamics inone-dimensional unbounded space and show how one recovers in the continuouslimits results for diffusion with resetting. The resetting dynamics of biasedrandom walker in one-dimensional domain bounded with periodic and reflectingboundaries is also analyzed. Depending on the bias the first-passageprobability in periodic domain shows multi-fold non-monotonicity as $r$ isvaried. Finally, we apply our formalism to study the transmission dynamics oftwo lattice walkers with resetting in one-dimensional domain bounded byperiodic and reflecting boundaries. The probability of a definite transmissionbetween the walkers shows non-monotonic behavior as the resetting probabilitiesare varied.

Discrete space-time resetting model: Application to first-passage and transmission statistics