Transition to shocks in TASEP and decoupling of last passage times

P. Nejjar, Latin American Journal of Probability and Mathematical Statistics 15 (2018) 1311–1334.

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Abstract
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.
Publishing Year
Date Published
2018-10-01
Journal Title
Latin American Journal of Probability and Mathematical Statistics
Volume
15
Issue
2
Page
1311-1334
ISSN
IST-REx-ID
70

Cite this

Nejjar P. Transition to shocks in TASEP and decoupling of last passage times. Latin American Journal of Probability and Mathematical Statistics. 2018;15(2):1311-1334. doi:10.30757/ALEA.v15-49
Nejjar, P. (2018). Transition to shocks in TASEP and decoupling of last passage times. Latin American Journal of Probability and Mathematical Statistics, 15(2), 1311–1334. https://doi.org/10.30757/ALEA.v15-49
Nejjar, Peter. “Transition to Shocks in TASEP and Decoupling of Last Passage Times.” Latin American Journal of Probability and Mathematical Statistics 15, no. 2 (2018): 1311–34. https://doi.org/10.30757/ALEA.v15-49.
P. Nejjar, “Transition to shocks in TASEP and decoupling of last passage times,” Latin American Journal of Probability and Mathematical Statistics, vol. 15, no. 2, pp. 1311–1334, 2018.
Nejjar P. 2018. Transition to shocks in TASEP and decoupling of last passage times. Latin American Journal of Probability and Mathematical Statistics. 15(2), 1311–1334.
Nejjar, Peter. “Transition to Shocks in TASEP and Decoupling of Last Passage Times.” Latin American Journal of Probability and Mathematical Statistics, vol. 15, no. 2, ALEA, 2018, pp. 1311–34, doi:10.30757/ALEA.v15-49.
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