Collective behavior of coupled multiplicative processes with stochastic resetting

A dynamical variable driven by the combination of a deterministic multiplicative process with stochastic reset events develops, at long times, a stationary power-law distribution. Here, we analyze how such distribution changes when several variables of the same kind interact with each other through diffusion-like coupling. While for weak coupling the variables are still distributed following power-law functions, their distributions are severely distorted as interactions become stronger, with sudden appearance of cutoffs and divergent singularities. We explore these effects both analytically and numerically, for coupled ensembles of identical and non-identical variables. The most relevant consequences of ensemble heterogeneity are assessed, and preliminary results for spatially distributed ensembles are presented.