Abstract
AbstractWe consider the asymmetric simple exclusion process (ASEP) on $${\mathbb {Z}}$$
Z
with a single second class particle initially at the origin. The first class particles form two rarefaction fans which come together at the origin, where the large time density jumps from 0 to 1. We are interested in X(t), the position of the second class particle at time t. We show that, under the KPZ 1/3 scaling, X(t) is asymptotically distributed as the difference of two independent, $${\mathrm {GUE}}$$
GUE
-distributed random variables. The key part of the proof is to show that X(t) equals, up to a negligible term, the difference of a random number of holes and particles, with the randomness built up by ASEP itself. This provides a KPZ analogue to the 1994 result of Ferrari and Fontes (Probab Theory Relat Fields 99:305–319, 1994), where this randomness comes from the initial data and leads to Gaussian limit laws.
Funder
Deutsche Forschungsgemeinschaft
Publisher
Springer Science and Business Media LLC
Subject
Mathematical Physics,Statistical and Nonlinear Physics
Reference23 articles.
1. Balazs, M., Bowen, R.: Product blocking measures and a particle system proof of the Jacobi triple product. Ann. Inst. Henri Poincaré Probab. Stat. (B) 54(1), 514–528 (2018)
2. Benjamini, I., Berger, N., Hoffman, C., Mossel, E.: Mixing times of the biased card shuffling and the asymmetric exclusion process. Trans. Am. Soc. 357(8), 3013–3029 (2005)
3. Borodin, A., Bufetov, A.: Color-position symmetry in interacting particle systems (2019). arXiv:1905.04692
4. Corwin, I.: The Kardar–Parisi–Zhang equation and universality class. Random Matrices Appl. 1(1), 76 (2012)
5. Corwin, I., Ferrari, P.L., Péché, S.: Universality of slow decorrelation in KPZ models. Ann. Inst. Henri Poincaré Probab. Stat. 48(1), 134–150 (2012)
Cited by
11 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献