%0 Generic %1 nica2020onesided %A Nica, Mihai %A Quastel, Jeremy %A Remenik, Daniel %D 2020 %K KPZ %T One-sided reflected Brownian motions and the KPZ fixed point %U http://arxiv.org/abs/2002.02922 %X We show that the system of one-sided reflected Brownian motions considered in WFS17 has integrable transition probabilities, expressed in terms of Hermite polynomials and hitting times of exponential random walks, and converges in the 1:2:3 scaling limit to the KPZ fixed point, the scaling invariant Markov process defined in MQR17 and believed to govern the long time large scale fluctuations for all models in the KPZ universality class. The reflected Brownian motion system is in variational duality to Brownian last passage percolation, shown recently in DOV18 to converge to the Airy sheet (or directed landscape), defined there as a strong limit of a functional of the Airy line ensemble. This establishes the variational formula for the KPZ fixed point in terms of the Airy sheet.

@misc{nica2020onesided, abstract = {We show that the system of one-sided reflected Brownian motions considered in [WFS17] has integrable transition probabilities, expressed in terms of Hermite polynomials and hitting times of exponential random walks, and converges in the 1:2:3 scaling limit to the KPZ fixed point, the scaling invariant Markov process defined in [MQR17] and believed to govern the long time large scale fluctuations for all models in the KPZ universality class. The reflected Brownian motion system is in variational duality to Brownian last passage percolation, shown recently in [DOV18] to converge to the Airy sheet (or directed landscape), defined there as a strong limit of a functional of the Airy line ensemble. This establishes the variational formula for the KPZ fixed point in terms of the Airy sheet.}, added-at = {2020-02-10T17:17:39.000+0100}, author = {Nica, Mihai and Quastel, Jeremy and Remenik, Daniel}, biburl = {https://www.bibsonomy.org/bibtex/222191e08597673ba7ff54631a8f7ee31/gzhou}, description = {One-sided reflected Brownian motions and the KPZ fixed point}, interhash = {96a53db3c531115a48dbebf62940f998}, intrahash = {22191e08597673ba7ff54631a8f7ee31}, keywords = {KPZ}, note = {cite arxiv:2002.02922}, timestamp = {2020-02-10T17:17:39.000+0100}, title = {One-sided reflected Brownian motions and the KPZ fixed point}, url = {http://arxiv.org/abs/2002.02922}, year = 2020 }