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Large N limit of the ratio of Lukyanov integrals
Abstract
We study the large-N asymptotics of ratios of Lukyanov integrals for fixed real coupling b≥1. Our approach uses their biorthogonal ensemble structure and vector Riemann--Hilbert techniques. Under stated analytic hypotheses, we derive the logarithmic ratio through its constant term, which is expressed by a Fredholm determinant. The expansion is locally uniform in the real parameter α and is formulated separately for even and odd particle numbers. We verify the hypotheses for the correction defined by the physical ground-state thermodynamic Bethe ansatz. The relation to quantum-field-theoretic one-point functions is discussed separately.
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BibTeX
@misc{wang2026large,
title = {{Large $N$ limit of the ratio of Lukyanov integrals}},
author = {Dong Wang},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.00662},
eprint = {2611.00662},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.00662},
}
RIS
TY - UNPB
TI - Large N limit of the ratio of Lukyanov integrals
AU - Dong Wang
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.00662
UR - https://arxiv.org/abs/2611.00662
AB - We study the large-N asymptotics of ratios of Lukyanov integrals for fixed real coupling b≥1. Our approach uses their biorthogonal ensemble structure and vector Riemann--Hilbert techniques. Under stated analytic hypotheses, we derive the logarithmic ratio through its constant term, which is expressed by a Fredholm determinant. The expansion is locally uniform in the real parameter α and is formulated separately for even and odd particle numbers. We verify the hypotheses for the correction defined by the physical ground-state thermodynamic Bethe ansatz. The relation to quantum-field-theoretic one-point functions is discussed separately.
ER -