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2015 Point-interacting Brownian motions in the KPZ universality class
Herbert Spohn, Tomohiro Sasamoto
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Electron. J. Probab. 20: 1-28 (2015). DOI: 10.1214/EJP.v20-3926

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.

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Herbert Spohn. Tomohiro Sasamoto. "Point-interacting Brownian motions in the KPZ universality class." Electron. J. Probab. 20 1 - 28, 2015. https://doi.org/10.1214/EJP.v20-3926

Information

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

zbMATH: 1328.60218
MathSciNet: MR3391870
Digital Object Identifier: 10.1214/EJP.v20-3926

Subjects:
Primary: 60K35
Secondary: 82C22, 82C24

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