In this article we study the Atlas model, which constitutes of Brownian particles on $ \mathbb{R} $, independent except that the Atlas (i.e., lowest ranked) particle $ X_{(1)}(t) $ receive drift $ ��dt $, $ ��\in\mathbb{R} $. For any fixed shape parameter $ a>2��_- $, we show that, up to a shift $ \frac{a}{2}t $, the entire particle system has an invariant distribution $ ��_a $, written in terms an explicit Radon-Nikodym derivative with respect to the Poisson point process of density $ a e^{a��} d��$. We further show that $ ��_a $ indeed has the product-of-exponential gap distribution $ ��_a $ derived in Sarantsev and Tsai (2016). As a simple application, we establish a bound on the fluctuation of the Atlas particle $ X_{(1)}(t) $ uniformly in $ t $, with the gaps initiated from $ ��_a $ and $ X_{(1)}(0)=0 $.

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