A PDE for the multi-time joint probability of the Airy process
Dong Wang
TL;DR
This paper derives a partial differential equation for the multi-time joint probability of the Airy process, extending previous results from the 2-time case and including a PDE for Dyson Brownian motion.
Contribution
It introduces a PDE for the multi-time joint probability of the Airy process, generalizing earlier 2-time results and connecting to Dyson Brownian motion.
Findings
Derived PDE for multi-time joint probability of Airy process
Extended PDE framework to Dyson Brownian motion
Generalized previous 2-time case results
Abstract
This paper gives a PDE for multi-time joint probability of the Airy process, which generalizes Adler and van Moerbeke's result on the 2-time case. As an intermediate step, the PDE for the multi-time joint probability of the Dyson Brownian motion is also given.
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Taxonomy
TopicsRandom Matrices and Applications · Stochastic processes and statistical mechanics · Statistical Methods and Bayesian Inference