# Stationary distributions of the Atlas model

@article{Tsai2018StationaryDO,
title={Stationary distributions of the Atlas model},
author={Li-Cheng Tsai},
journal={Electronic Communications in Probability},
year={2018},
volume={23},
pages={10}
}
• 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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