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Register a new userThe TAZRP speed process
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In [AAV] Amir, Angel and Valk{o} studied a multi-type version of the totally asymmetric simple exclusion process (TASEP) and introduced the TASEP speed process, which allowed them to answer delicate questions about the joint distribution of the speed of several second-class particles in the TASEP rarefaction fan. In this paper we introduce the analogue of the TASEP speed process for the totally asymmetric zero-range process (TAZRP), and use it to obtain new results on the joint distribution of the speed of several second-class particles in the TAZRP with a reservoir. There is a close link from the speed process to questions about stationary distributions of multi-ty
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In the multi-type totally asymmetric simple exclusion process (TASEP) on the line, each site of Z is occupied by a particle labeled with some number, and two neighboring particles are interchanged at rate one if their labels are in increasing order. Consider the process with the initial configuration where each particle is labeled by its position. It is known that in this case a.s. each particle has an asymptotic speed which is distributed uniformly on [-1,1]. We study the joint distribution of these speeds: the TASEP speed process. We prove that the TASEP speed process is stationary with respect to the multi-type TASEP dynamics. Consequently, every ergodic stationary measure is given as a projection of the speed process measure. This generalizes previous descriptions restricted to finitely many classes. By combining this result with known stationary measures for TASEPs with finitely many types, we compute several marginals of the speed process, including the joint density of two and three consecutive speeds. One striking property of the distribution is that two speeds are equal with positive probability and for any given particle there are infinitely many others with the same speed. We also study the partially asymmetric simple exclusion process (ASEP). We prove that the states of the ASEP with the above initial configuration, seen as permutations of Z, are symmetric in distribution. This allows us to extend some of our results, including the stationarity and description of all ergodic stationary measures, also to the ASEP.
In this paper, we obtain the transition probability formulas for the Asymmetric Simple Exclusion Process (ASEP) and the $q$-deformed Totally Asymmetric Zero Range Process ($q$-TAZRP) on the ring by applying the coordinate Bethe ansatz. We also compute the distribution function for a tagged particle with general initial condition.
We give overcrowding estimates for the Sine_beta process, the bulk point process limit of the Gaussian beta-ensemble. We show that the probability of having at least n points in a fixed interval is given by $e^{-frac{beta}{2} n^2 log(n)+O(n^2)}$ as $nto infty$. We also identify the next order term in the exponent if the size of the interval goes to zero.
We study the multipoint distribution of stationary half-space last passage percolation with exponentially weighted times. We derive both finite-size and asymptotic results for this distribution. In the latter case we observe a new one-parameter process we call half-space Airy stat. It is a one-parameter generalization of the Airy stat process of Baik-Ferrari-Peche, which is recovered far away from the diagonal. All these results extend the one-point results previously proven by the authors.
Strong negative dependence properties have recently been proved for the symmetric exclusion process. In this paper, we apply these results to prove convergence to the Poisson and normal distributions for various functionals of the process.
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