The Inert Drift Atlas Model

Consider a massive (inert) particle impinged from above by N Brownian particles that are instantaneously reflected upon collision with the inert particle. The velocity of increases due to influence an external Newtonian potential (e.g. gravitation) and decreases in proportion total local time collisions particles. This system models semi-permeable membrane fluid having microscopic impurities (Knight Probab Theory Relat Fields 121:577–598, 2001). We study long-time behavior process $$(V,{\textbf{Z}})$$ , where V is $${\textbf{Z}}$$ vector gaps between successive ordered their relative positions. not hypoelliptic, reversible, has singular form interactions. Thus stability requires new ideas. show this unique stationary distribution takes explicit product which Gaussian component exponential other components. also convergence variation distance happens at rate. further obtain certain law large numbers results for locations intersection times.