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Near-optimal bounds for the critical 2d SHF and the delta-Bose gas
Abstract
We establish a near-optimal upper bound exp(exp(CN1+o(1))) for the N-th moment of the critical two-dimensional stochastic heat flow, improving on the bound exp(exp(CN2)) of Gu, Quastel, and Tsai. Near-optimality follows from the lower bound exp(exp(cN)) of Ganguly and Nam. These estimates establish the exponential scale of the ground-state energy of the two-dimensional N-body delta-Bose gas predicted by Rajeev's conjecture, up to a vanishing error in the exponent. As a further step toward this conjecture, we derive, for each fixed N, a formula for the ground-state energy in terms of the bottom of the spectrum of a principal operator.
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BibTeX
@misc{li2026nearoptimal,
title = {{Near-optimal bounds for the critical 2d SHF and the delta-Bose gas}},
author = {Xue-Mei Li and Te-Chun Wang},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.03191},
eprint = {2611.03191},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.03191},
}
RIS
TY - UNPB
TI - Near-optimal bounds for the critical 2d SHF and the delta-Bose gas
AU - Xue-Mei Li
AU - Te-Chun Wang
PY - 2026
DA - 2026/11/02
PB - arXiv
DO - 10.48550/arxiv.2611.03191
UR - https://arxiv.org/abs/2611.03191
AB - We establish a near-optimal upper bound exp(exp(CN^1+o(1))) for the N-th moment of the critical two-dimensional stochastic heat flow, improving on the bound exp(exp(CN^2)) of Gu, Quastel, and Tsai. Near-optimality follows from the lower bound exp(exp(cN)) of Ganguly and Nam. These estimates establish the exponential scale of the ground-state energy of the two-dimensional N-body delta-Bose gas predicted by Rajeev's conjecture, up to a vanishing error in the exponent. As a further step toward this conjecture, we derive, for each fixed N, a formula for the ground-state energy in terms of the bottom of the spectrum of a principal operator.
ER -