Perturbed GUE Minor Process and Warren's Process with Drifts
Mathematical Physics
2014-04-24 v3 math.MP
Probability
Abstract
We consider the minor process of (Hermitian) matrix diffusions with constant diagonal drifts. At any given time, this process is determinantal and we provide an explicit expression for its correlation kernel. This is a measure on the Gelfand-Tsetlin pattern that also appears in a generalization of Warren's process, in which Brownian motions have level-dependent drifts. Finally, we show that this process arises in a diffusion scaling limit from an interacting particle system in the anisotropic KPZ class in 2+1 dimensions. Our results generalize the known results for the zero drift situation.
Keywords
Cite
@article{arxiv.1212.5534,
title = {Perturbed GUE Minor Process and Warren's Process with Drifts},
author = {Patrik L. Ferrari and René Frings},
journal= {arXiv preprint arXiv:1212.5534},
year = {2014}
}
Comments
28 pages, 3 figures; The result for the system of BM is now lifted to a theorem