  Millimeter wave (mmWave) has attracted considerable attention due to its wide
bandwidth and high frequency. However, it is highly susceptible to blockages,
resulting in significant degradation of the coverage and the sum rate. A
promising approach is deploying distributed reconfigurable intelligent surfaces
(RISs), which can establish extra communication links. In this paper, we
investigate the impact of distributed RISs on the coverage probability and the
sum rate in mmWave wireless communication systems. Specifically, we first
introduce the system model, which includes the blockage, the RIS and the user
distribution models, leveraging the Poisson point process. Then, we define the
association criterion and derive the conditional coverage probabilities for the
two cases of direct association and reflective association through RISs.
Finally, we combine the two cases using Campbell's theorem and the total
probability theorem to obtain the closed-form expressions for the ergodic
coverage probability and the sum rate. Simulation results validate the
effectiveness of the proposed analytical approach, demonstrating that the
deployment of distributed RISs significantly improves the ergodic coverage
probability by 45.4% and the sum rate by over 1.5 times.
