An analytic derivation of the empirical correlations of gamma-ray bursts Fan Xu, Yong-Feng Huang, Jin-Jun Geng, Xue-Feng Wu, Xiu-Juan Li and Zhi-Bin Zhang A&A, 673 (2023) A20 Published online: 26 April 2023 DOI: 10.1051/0004-6361/202245414