{"ID":2890486,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.19215","arxiv_id":"2507.19215","title":"On a $T_1$ Transport inequality for the adapted Wasserstein distance","abstract":"The $L^1$ transport-entropy inequality (or $T_1$ inequality), which bounds the $1$-Wasserstein distance in terms of the relative entropy, is known to characterize Gaussian concentration. To extend the $T_1$ inequality to laws of discrete-time processes while preserving their temporal structure, we investigate the adapted $T_1$ inequality which relates the $1$-adapted Wasserstein distance to the relative entropy. Building on the Bolley--Villani inequality, we establish the adapted $T_1$ inequality under the same moment assumption as the classical $T_1$ inequality.","short_abstract":"The $L^1$ transport-entropy inequality (or $T_1$ inequality), which bounds the $1$-Wasserstein distance in terms of the relative entropy, is known to characterize Gaussian concentration. To extend the $T_1$ inequality to laws of discrete-time processes while preserving their temporal structure, we investigate the adapt...","url_abs":"https://arxiv.org/abs/2507.19215","url_pdf":"https://arxiv.org/pdf/2507.19215v2","authors":"[\"Jonghwa Park\"]","published":"2025-07-25T12:36:47Z","proceeding":"math.PR","tasks":"[\"math.PR\",\"math.ST\"]","methods":"[]","has_code":false}