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Reducing the domain of discrete multi-time determinantal point processes
Abstract
We consider a class of discrete multi-time determinantal point processes whose correlation kernels admit a double-contour integral form, containing Schur processes as simple examples. We show that the form of the correlation kernel is preserved under conditioning of the point process to a restricted domain, however, with an integrand which becomes more complicated and which is characterized by a Riemann-Hilbert problem. We apply our general result to domino tilings of reduced Aztec diamonds and to lozenge tilings of hexagons with holes. Our results show a striking analogy with the Its-Izergin-Korepin-Slavnov method for integrable kernels.
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BibTeX
@misc{claeys2026reducing,
title = {{Reducing the domain of discrete multi-time determinantal point processes}},
author = {Tom Claeys and Felix Gideonse},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.28131},
eprint = {2608.28131},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.28131},
}
RIS
TY - UNPB
TI - Reducing the domain of discrete multi-time determinantal point processes
AU - Tom Claeys
AU - Felix Gideonse
PY - 2026
DA - 2026/08/28
PB - arXiv
DO - 10.48550/arxiv.2608.28131
UR - https://arxiv.org/abs/2608.28131
AB - We consider a class of discrete multi-time determinantal point processes whose correlation kernels admit a double-contour integral form, containing Schur processes as simple examples. We show that the form of the correlation kernel is preserved under conditioning of the point process to a restricted domain, however, with an integrand which becomes more complicated and which is characterized by a Riemann-Hilbert problem. We apply our general result to domino tilings of reduced Aztec diamonds and to lozenge tilings of hexagons with holes. Our results show a striking analogy with the Its-Izergin-Korepin-Slavnov method for integrable kernels.
ER -