Electronic Journal of Probability

Point-interacting Brownian motions in the KPZ universality class

Herbert Spohn and Tomohiro Sasamoto

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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

nonreversible interacting diffusion processes asymptotic analysis

This work is licensed under aCreative Commons Attribution 3.0 License.


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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