The Brownian Vacancy Driven Walk

Details The Brownian Vacancy Driven Walk The Brownian Vacancy Driven Walk

1998-04-20

arxiv.org/abs/cond-mat/9804220v1

Intl.J.Mod.Phys. B, Vol 11, (1997) 3343-3374

Physics

Condensed Matter

Statistical Mechanics

29 pages (Latex), 3 postscript figures embedded

Scientific paper

We investigate the lattice walk performed by a tagged member of an infinite `sea' of particles filling a d-dimensional lattice, in the presence of a Brownian vacancy. Particle-particle exchange is forbidden; the only interaction between them being hard core exclusion. The tagged particle, differing from the others only by its tag, moves only when it exchanges places with the hole. In this sense, it is a lattice walk ``driven'' by the Brownian vacancy. The probability distributions for its displacement and for the number of steps taken, after $n$-steps of the vacancy, are derived. Surprisingly, none of them is a Gaussian! It is shown that the only nontrivial dimension where the walk is recurrent is d=2.

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