Mixing-time comparison between ASEP and homogeneous PushTASEP

Determine which of the homogeneous multispecies ASEP and the homogeneous multispecies t-PushTASEP mixes faster, meaning converges more rapidly to their common stationary distribution when started from the same initial condition.

Background

The paper proves that the homogeneous multispecies ASEP and homogeneous multispecies t-PushTASEP commute because both arise from the same family of commuting transfer matrices. Consequently, the two processes share eigenstates, and their common stationary distribution is a joint eigenstate of the transfer matrices. Although the stationary distribution is therefore identified as common to both models, the paper does not resolve whether their convergence rates from identical initial configurations differ, nor which process has the faster mixing behavior.

References

It also gives rise to an interesting question; which one among the ASEP and the homogeneous PushTASEP mixes faster, i.e. converges faster to their common stationary distribution starting from the same initial condition.

— Multispecies inhomogeneous $t$-PushTASEP from antisymmetric fusion  (2503.00829 - Ayyer et al., 2 Mar 2025) in Page 2, Section 1 (Introduction)