Large language model (LLM) agents increasingly serve as computational actors in multi-agent social simulations. While existing work emphasizes representative personas and average-case behavior, social science shows that persistent tail actors can disproportionately shape collective dynamics. We study this regularity in controlled LLM-based multi-agent systems (LLM-MAS). In these systems, such actors cannot be reduced to fixed scalar states: prompts, natural-language histories, and backbone generation mediate their behavior and influence. We first analyzed three properties of extremists in sociology and model the LLM extremist based on LLM-native perspective. We introduce EXAM, an EXtremist Agent Modeling framework that capable of configuring extremist agents for specific tasks and precisely controlling their population proportion, spatial distribution, interaction protocols, and measurement interfaces. Across four scenarios: congressional election, financial crisis, epidemic public opinion, and iterated prisoner's dilemma, we observe that small persistent tail groups produce measurable, backbone- and scenario-dependent collective shifts. EXAM shows how this social-science regularity manifests through language-mediated mechanisms specific to LLM-based social simulation.

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