Alcohol-related violence remains a serious social and public health problem in the United States. A large corpus of work suggests a positive statistical relationship between alcohol outlet density and violence. However, questions remain as to how neighborhood violence evolves in response to varying access to alcohol outlets. This paper introduces an approach for analyzing the spatial and temporal dynamics of violence and its association with alcohol outlets by embedding the evolution of assault events and outlet density within a spatially heterogeneous Markov chain framework. This framework enables the exploration of spatiotemporal dynamics of alcohol outlets and violence and controls for potentially confounding impacts and spatial heterogeneity. Using a case study at the block group level in Seattle, Washington, the results of this paper suggest that violence is spatially heterogeneous at the local level and locations with sparsely distributed alcohol outlets are less likely to see an increase in violence when compared to areas with higher densities of outlets. Further, the modeling approach helps identify locations that might ``tip'' into more violent conditions if more outlets were allowed to operate. This paper concludes with a brief discussion of how the methods and results can help improve the management, licensing, and policy development for alcohol outlets in a community.