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Recently, the study of social conventions has attracted much attention in the literature. We notice that a type of interesting phenomena, local convention phenomena, may also exist in certain multi-agent systems. When agents are partitioned into compact communities, different local conventions emerge in different communities. In this paper, we provide a definition for local conventions, and propose two metrics measuring their strength and diversity. In our experimental study, we show that agents can achieve coordination via establishing diverse stable local conventions, which indicates a practical way to solve coordination problems other than the traditional global convention emergence. Moreover, we find that with smaller community sizes, denser connections and fewer available actions, diverse local conventions emerge in shorter time.