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Stochastics Seminar: Sayan Banerjee , UNC-Chapel Hill, Ergodicity and fluctuations of the Atlas model
Stochastics Seminar: Sayan Banerjee , UNC-Chapel Hill, Ergodicity and fluctuations of the Atlas model
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…