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The TASEP is a paradigmatic model of out-of-equilibrium statistical physics, for which many quantities have been computed, either exactly or by approximate methods. In this work we study two new kinds of observables that have some relevance in biological or traffic models. They represent the probability for a given clearance zone of the lattice to be empty (for the first time) at a given time, starting from a step density profile. Exact expressions are obtained for single-time quantities, while more involved history-dependent observables are studied by Monte Carlo simulation, and partially predicted by a phenomenological approach.
We consider the totally asymmetric simple exclusion process (TASEP) with non-random initial condition having density $rho$ on $mathbb{Z}_-$ and $lambda$ on $mathbb{Z}_+$, and a second class particle initially at the origin. For $rho<lambda$, there is
We consider the one-dimensional totally asymmetric simple exclusion process with an arbitrary initial condition in a spatially periodic domain, and obtain explicit formulas for the multi-point distributions in the space-time plane. The formulas are g
We present an explicit representation for the matrix product ansatz for some two-species TASEP with open boundary conditions. The construction relies on the integrability of the models, a property that constrains the possible rates at the boundaries.
We study a totally asymmetric simple exclusion process (TASEP) with one defect site, hopping rate $q<1$, near the system boundary. Regarding our system as a pair of uniform TASEPs coupled through the defect, we study various methods to match a emph{f
We study the effect of single biased tracer particle in a bath of other particles performing the random average process (RAP) on an infinite line. We focus on the large time behavior of the mean and the fluctuations of the positions of the particles