Stationary distributions of the Atlas model

  title={Stationary distributions of the Atlas model},
  author={Li-Cheng Tsai},
  journal={Electronic Communications in Probability},
  • Li-Cheng Tsai
  • Published 2018
  • Mathematics
  • Electronic Communications in Probability
  • 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 $ \gamma dt $, $ \gamma\in\mathbb{R} $. For any fixed shape parameter $ a>2\gamma_- $, we show that, up to a shift $ \frac{a}{2}t $, the entire particle system has an invariant distribution $ \nu_a $, written in terms an explicit Radon-Nikodym derivative with respect to the Poisson point process of… CONTINUE READING
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