Transition to shocks in TASEP and decoupling of last passage times - Nejjar, Peter; Random matrices, universality and disordered quantum systems; Optimal Transport and Stochastic Dynamics (Latin American Journal of Probability and Mathematical Statistics, 2018)
We consider the totally asymmetric simple exclusion process in a critical scaling parametrized by a≥0, which creates a shock in the particle density of order aT−1/3, T the observation time. When starting from step initial data, we provide bounds on the limiting law which in particular imply that in the double limit lima→∞limT→∞ one recovers the product limit law and the degeneration of the correlation length observed at shocks of order 1. This result is shown to apply to a general last-passage percolation model. We also obtain bounds on the two-point functions of several airy processes.
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