  The millimeter wave (mmWave) has received considerable interest due to its
expansive bandwidth and high frequency. However, a noteworthy challenge arises
from its vulnerability to blockages, leading to reduced coverage and achievable
rates. To address these limitations, a potential solution is to deploy
distributed reconfigurable intelligent surfaces (RISs), which comprise many
low-cost and passively reflected elements, and can facilitate the establishment
of extra communication links. In this paper, we leverage stochastic geometry to
investigate the ergodic coverage probability and the achievable rate in both
distributed RISs-assisted single-cell and multi-cell mmWave wireless
communication systems. Specifically, we first establish the system model
considering the stochastically distributed blockages, RISs and users by the
Poisson point process. Then we give the association criterion and derive the
association probabilities, the distance distributions, and the conditional
coverage probabilities for two cases of associations between base stations and
users without or with RISs. Finally, we use Campbell's theorem and the total
probability theorem to obtain the closed-form expressions of the ergodic
coverage probability and the achievable rate. Simulation results verify the
effectiveness of our analysis method, and demonstrate that by deploying
distributed RISs, the ergodic coverage probability is significantly improved by
approximately 50%, and the achievable rate is increased by more than 1.5 times.
