A. Bufetov and P. Nejjar Shock fluctuations in TASEP under a variety of time scalings arXiv:2003.12414 2020 https://arxiv.org/abs/2003.12414
Abstract: We consider the totally asymmetric simple exclusion process (TASEP) with two different initial conditions with shock discontinuities, made by block of fully packed particles. Initially a second class particle is at the left of a shock discontinuity. Using multicolored TASEP we derive an exact formulas for the distribution of the second class particle and colored height functions. These are given in terms of the height function at different positions of a single TASEP configuration. We study the limiting distributions of second class particles (and colored height functions). The result depends on how the width blocks of particles scale with the observation time; we study a variety of such scalings.
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A. Borodin, A. Bufetov and P.L. Ferrari TASEP with a moving wall preprint: arXiv:2111.02530 0 http://arxiv.org/abs/2111.02530
Abstract: We consider a totally asymmetric simple exclusion on Z with the step initial condition, under the additional restriction that the first particle cannot cross a deterministally moving wall. We prove that such a wall may induce asymptotic fluctuation distributions of particle positions of the form P(supÏâR{Airy2(Ï)âg(Ï)}â¤S) with arbitrary barrier functions g. This is the same class of distributions that arises as one-point asymptotic fluctuations of TASEPs with arbitrary initial conditions. Examples include Tracy-Widom GOE and GUE distributions, as well as a crossover between them, all arising from various particles behind a linearly moving wall. We also prove that if the right-most particle is second class, and a linearly moving wall is shock-inducing, then the asymptotic distribution of the position of the second class particle is a mixture of the uniform distribution on a segment and the atomic measure at its right end.