  Microrheology is the study of the properties of a complex fluid through the
diffusion dynamics of small particles, typically latex beads, moving through
that material. Currently, it is the dominant technique in the study of the
physical properties of biological fluids, of the material properties of
membranes or the cytoplasm of cells, or of the entire cell. The theoretical
underpinning of microrheology was given in Mason and Weitz (Physical Review
Letters; 1995), who introduced a framework for the use of path data of
diffusing particles to infer viscoelastic properties of its fluid environment.
The multi-particle tracking techniques that were subsequently developed have
presented numerous challenges for experimentalists and theoreticians. This
paper describes some specific challenges that await the attention of
statisticians and applied probabilists. We describe relevant aspects of the
physical theory, current inferential efforts and simulation aspects of a
central model for the dynamics of nano-scale particles in viscoelastic fluids,
the generalized Langevin equation.
