A note on the diffusivity of finite-range asymmetric exclusion processes on Z

Abstract

The diffusivity $D(t)$ of finite-range asymmetric exclusion processes on $\mathbb{Z}$ with non-zero drift is expected to be of order $t^{1/3}$. Seppäläinen and Balázs recently proved this conjecture for the nearest neighbor case. We extend their results to general finite range exclusion by proving that the Laplace transform of the diffusivity is of the conjectured order. We also obtain a pointwise upper bound for $D(t)$ the correct order.

References in corpus (2)

• Scaling Limit for the Space-Time Covariance of the Stationary Totally Asymmetric Simple Exclusion Process
• Second class particles and cube root asymptotics for Hammersley's process

Cited by in corpus (5)

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• On microscopic derivation of a fractional stochastic Burgers equation
• Order of current variance and diffusivity in the rate one totally asymmetric zero range process
• The stationary AKPZ equation: logarithmic superdiffusivity
• Diffusivity of lattice gases