Central Limit Theorem for a Tagged Particle in Asymmetric Simple Exclusion

Details Central Limit Theorem for a Tagged Particle in Asymmetric Simple Exclusion Central Limit Theorem for a Tagged Particle in Asymmetric Simple Exclusion

2006-11-16

arxiv.org/abs/math/0611505v2

Mathematics

Probability

28 pages, no figures

Scientific paper

We prove a Functional Central Limit Theorem for the position of a Tagged Particle in the one-dimensional Asymmetric Simple Exclusion Process in the hyperbolic scaling, starting from a Bernoulli product measure conditioned to have a particle at the origin. We also prove that the position of the Tagged Particle at time $t$ depends on the initial configuration, by the number of empty sites in the interval $[0,(p-q)\alpha t]$ divided by $\alpha$ in the hyperbolic and in a longer time scale, namely $N^{4/3}$.

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