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arXiv · 1411.3142

Point-interacting Brownian motions in the KPZ universality class

Tomohiro Sasamoto·Herbert Spohn
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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 positive time. A formal asymptotics for this determinant establishes the link to the Kardar-Parisi-Zhang universality class.

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Tomohiro Sasamoto, Herbert Spohn. 2014-11-12. Point-interacting Brownian motions in the KPZ universality class. https://arxiv.org/abs/1411.3142

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