Electronic Journal of Probability

Point-interacting Brownian motions in the KPZ universality class

Herbert Spohn and Tomohiro Sasamoto

Full-text: Open access

Abstract

We discuss chains of interacting Brownian motions. Their time reversal invariance is broken because of asymmetry in the interaction strength between left and right neighbor. In the limit of a very steep and short range potential one arrives at Brownian motions with oblique reflections. For this model we prove a Bethe ansatz formula for the transition probability and self-duality. In case of half-Poisson initial data, duality is used to arrive at a Fredholm determinant for the generating function of the number of particles to the left of some reference point at any time $t > 0$. A formal asymptotics for this determinant establishes the link to the Kardar-Parisi-Zhang universality class.

Article information

Source
Electron. J. Probab., Volume 20 (2015), paper no. 87, 28 pp.

Dates
Accepted: 28 August 2015
First available in Project Euclid: 4 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1465067193

Digital Object Identifier
doi:10.1214/EJP.v20-3926

Mathematical Reviews number (MathSciNet)
MR3391870

Zentralblatt MATH identifier
1328.60218

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 82C22: Interacting particle systems [See also 60K35] 82C24: Interface problems; diffusion-limited aggregation

Keywords
nonreversible interacting diffusion processes asymptotic analysis

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Spohn, Herbert; Sasamoto, Tomohiro. Point-interacting Brownian motions in the KPZ universality class. Electron. J. Probab. 20 (2015), paper no. 87, 28 pp. doi:10.1214/EJP.v20-3926. https://projecteuclid.org/euclid.ejp/1465067193


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