Determinantal structures in space inhomogeneous dynamics on interlacing arrays
arXiv:1910.09500 · doi:10.1007/s00023-019-00881-5
Abstract
We introduce a space inhomogeneous generalization of the dynamics on interlacing arrays considered by Borodin and Ferrari. We show that for a certain class of initial conditions the point process associated to the dynamics has determinantal correlation functions and we calculate explicitly, in the form of a double contour integral, the correlation kernel for one of the most classical initial conditions, the densely packed. En route to proving this we obtain some results of independent interest on non-intersecting general pure-birth chains, that generalize the Charlier process, the discrete analogue of Dyson's Brownian motion. Finally, these dynamics provide a coupling between the inhomogeneous versions of the TAZRP and PushTASEP particle systems which appear as projections on the left and right edges of the array respectively.
arXiv commentMinor improvements throughout. Published at Annales Henri Poincare
References in corpus (11)
- Shape Fluctuations and Random Matrices
- Fluctuation properties of the TASEP with periodic initial configuration
- Eynard-Mehta theorem, Schur process, and their pfaffian analogs
- Flows, coalescence and noise
- Anisotropic growth of random surfaces in 2+1 dimensions
- Directed polymers and the quantum Toda lattice
- An algebraic construction of duality functions for the stochastic U_q(A_n^{(1)}) vertex model and its degenerations
- Generalizations of TASEP in discrete and continuous inhomogeneous space
- A Multi-species ASEP(q,j) and q-TAZRP with Stochastic Duality
- Interlacing Diffusions
- A (2+1)-dimensional growth process with explicit stationary measures