In earlier work [Esaki, 2014, PJMI], Esaki obtained a continuous-time infinite-particle system on $\mathbb{Z}$ that is a discrete analogue of Dyson Brownian motion with $\beta = 2$. This system has a space-time determinantal structure, allowing various quantities to be computed and estimated explicitly; it is thus a so-called integrable stochastic system. Making full use of this structure, I will discuss a scaling limit for this infinite-particle system. This talk is based on joint work with Shota Esaki (Tokyo University of Science).