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Session 34. SPDE: stochastic analysis and dynamics
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Point-interacting Brownian motions in the KPZ universality class |
Herbert Spohn, Zentrum Mathematik, TU München, Germany
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The talk is based on the joint work with Tomohiro Sasamoto, Tokyo Institute of Technology, Japan
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We discuss chains of interacting Brownian motions, for which 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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