Fractional Brownian motion in interacting particle systems

Fractional Brownian motion (fBm) is the unique family of self-similar, one dimensional Gaussian processes, with stationary increments. While these properties make fBm a natural scaling limit, not many processes are known to have fBm as a continuum limit. In this talk we will discuss some models that do have fBM as a continuum limit such as the distribution of square free numbers, the tagged particle in the symmetric exclusion processes, the Hammond-Sheffield Urn, and voter models with long range correlation. This talk is based on the work https://arxiv.org/abs/2311.03662