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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


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.


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

Primary: 60K35
Secondary: 82C22, 82C24


Vol.20 • 2015
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