Abstract: A model of coupling discrete Markovian random walkers is studied. A pair of walkers are coupled. The distribution of arguments is updated to have higher probability pointing to its conjugate walker in each step. Increasing coupling strength slows down diffusion. Stochastic distribution of arguments rather than lengths dominates in this issue. Due to coupling, a pair of walkers arrive at some synchrony state. In some sense, it is the synchrony that induces diffusion slowing.

Key words: random walks, diffusion speed, coupling