We investigate the long-time behavior and stationary fluctuations of an infinite-dimensional rank-based diffusion process, called the Atlas model, where particles move as independent Brownian motions, with the lowest ranked particle at any time getting a unit upward drift. The associated process of gaps between successive ranked particles possesses an uncountable collection of invariant measures. We analyze Domains of Attraction (DoA) for each such state, that is, quantify starting configurations for which the gap distribution converges to a given steady state. We also furnish fluctuation results for the stationary particle system in the form of associated stochastic partial differential equations (SPDEs).

Based on joint works with Amarjit Budhiraja and Peter Rudzis.

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