OxTalks will soon move to the new Halo platform and will become 'Oxford Events.' There will be a need for an OxTalks freeze. This was previously planned for Friday 14th November – a new date will be shared as soon as it is available (full details will be available on the Staff Gateway).
In the meantime, the OxTalks site will remain active and events will continue to be published.
If staff have any questions about the Oxford Events launch, please contact halo@digital.ox.ac.uk
We present an explicit coupling of Brownian bridges plus affine shifts that are jointly invariant for the Kardar-Parisi-Zhang equation with periodic noise. These are described by Pitman-like transforms of independent Brownian bridges. We obtain these invariant measures by working with a semi-discrete model known as the O’Connell-Yor polymer in a periodic environment. In that setting, the relevant Markov process is described by a system of coupled SDEs. We show how to transform this Markov process to an auxiliary Markov process with a more tractable invariant measure. We discuss connections of this method to works of Ferrari and Martin in the mid 2000s in the context of multi-species particle systems. Furthermore, we present an application of this work to give an explicit formula for the covariance function of a limiting Gaussian process obtained from the coupled stochastic heat equation. Based on forthcoming joint work with Ivan Corwin and Yu Gu.
