Title: Kinetically constrained lattice gases: tagged particle diffusion,
Abstract: Kinetically constrained lattice gases (KCLG) are interacting particle systems
on the integer lattice $\mathbb Z^d$ with hard core exclusion and
Kawasaki type dynamics. Their peculiarity is that jumps are allowed only if
the configuration satisfies a constraint which asks for enough empty sites in a
certain local neighborhood. KCLG have been introduced and extensively studied
in physics literature as models of glassy dynamics. We focus on the most
studied class of KCLG, the Kob Andersen (KA) models. We analyze the behavior of
a tracer (i.e. a tagged particle) at equilibrium. We prove that for all
dimensions $d\geq 2$ and for any equilibrium particle density, under diffusive
rescaling the motion of the tracer converges to a $d$-dimensional Brownian
motion with non-degenerate diffusion matrix. Therefore we disprove the
occurrence of a diffusive/non diffusive transition which had been conjectured
in physics literature. Our technique is flexible enough and can be extended to
analyse the tracer behavior for other choices of constraints.