Dynamically correlated gas under resetting: exact results for general resetting protocols

In this thesis, we consider a one-dimensional gas of \( N \) independent Brownian particles subject to stochastic resetting, with inter-reset times drawn from a general waiting-time distribution \( \psi(\tau) \). This includes the well-known Poissonian case, where \( \psi(\tau)=re^{-r\tau} \), and extends to more general classes of resetting, such as heavy-tailed and bounded distributions. While our study is focused on the one-dimensional case, the main results are easily generalizable to higher dimensions. Exploiting the renewal structure of the resetting dynamics, we derive explicit analytical expressions for the non-equilibrium stationary state (NESS) and various observables of interest, including particle density, extreme value statistics, order statistics, gap statistics, and full counting statistics. We demonstrate that these observables take a scaling form that exhibits some universal scaling behaviors, characterized by scale factors independent of the specific resetting protocol. However, their detailed forms depend explicitly on the distribution of inter-reset times. Remarkably, we identify a novel class of extreme value statistics (EVS) not previously described in the literature. We classify the resetting protocols into three distinct universality classes based on the tail behavior of the resetting-time distribution: exponential decay, bounded support, and power-law tails. Our theoretical predictions are supported by numerical simulations. These results extend the understanding of resetting dynamics in many-body systems and offer new insights into non-equilibrium systems with strongly correlated degrees of freedom.