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Transverse momentum distributions of deuterons and antideuterons in Au + Au collisions at sNN=14.5, 62.4, and 200 GeV with different centrality are studied in the framework of the multisource thermal model. Transverse momentum spectra are conformably and approximately described by the Tsallis distribution. The dependence of parameters (average transverse momenta, effective temperature, and entropy index) on event centrality is obtained. It is found that the parameters T increase and q decrease with increase of the average number of particles involved in collisions, which reveals the transverse excitation degree increases with collision centrality.