Antishocks in the ASEP with open boundaries conditioned on low current (Q2843742)

This work considers an asymmetric simple exclusion process on a line, with jump rates \(c_r > c_l\), so that there is a bias towards the right, and with open boundaries at different densities \(\rho_l > \rho_r\) (respectively the densities at the left and at the right). In this situation, the stationary state is a non-equilibrium steady state, with a current of particles flowing from the side with higher densities to the one with lower density.NEWLINENEWLINEThe authors consider the dynamic with an initial data given by Bernoulli measures with average \(\rho_l\) on the left up to a site \(n\), and average \(\rho_r\) afterwards. They assume that the densities and the hopping asymmetry \(q = \sqrt{c_r/c_l}\) satisfy the relation \(\frac{\rho_l(1-\rho_r)}{\rho_r(1-\rho_l)} = q^2\). Such a profile manifests an antishock at site \(n\). The main result is that if the process is conditioned to having an anomalously low time-integrated current, then the antishock is stable. Moreover, the position of the antishock performs a biased random walk (with reflecting boundary condition).