article published yes Nicolas Clozeau author fea1b376-906f-11eb-847d-b2c0cf46455b Francesco Mattesini author JuFi department Bridging Scales in Random Materials project We study a random matching problem on closed compact 2 -dimensional Riemannian manifolds (with respect to the squared Riemannian distance), with samples of random points whose common law is absolutely continuous with respect to the volume measure with strictly positive and bounded density. We show that given two sequences of numbers n and m=m(n) of points, asymptotically equivalent as n goes to infinity, the optimal transport plan between the two empirical measures μn and νm is quantitatively well-approximated by (Id,exp(∇hn))#μn where hn solves a linear elliptic PDE obtained by a regularized first-order linearization of the Monge-Ampère equation. This is obtained in the case of samples of correlated random points for which a stretched exponential decay of the α -mixing coefficient holds and for a class of discrete-time Markov chains having a unique absolutely continuous invariant measure with respect to the volume measure. https://research-explorer.ista.ac.at/download/14797/18788/2024_ProbTheoryRelatFields_Clozeau.pdf application/pdfno Springer Nature2024 eng 0178-8051 1432-2064 2303.00353 00113620620000210.1007/s00440-023-01254-0 190485-541 N. Clozeau, F. Mattesini, Probability Theory and Related Fields 190 (2024) 485–541. Clozeau N, Mattesini F. 2024. Annealed quantitative estimates for the quadratic 2D-discrete random matching problem. Probability Theory and Related Fields. 190, 485–541. N. Clozeau and F. Mattesini, “Annealed quantitative estimates for the quadratic 2D-discrete random matching problem,” <i>Probability Theory and Related Fields</i>, vol. 190. Springer Nature, pp. 485–541, 2024. Clozeau, N., &#38; Mattesini, F. (2024). Annealed quantitative estimates for the quadratic 2D-discrete random matching problem. <i>Probability Theory and Related Fields</i>. Springer Nature. <a href="https://doi.org/10.1007/s00440-023-01254-0">https://doi.org/10.1007/s00440-023-01254-0</a> Clozeau, Nicolas, and Francesco Mattesini. “Annealed Quantitative Estimates for the Quadratic 2D-Discrete Random Matching Problem.” <i>Probability Theory and Related Fields</i>, vol. 190, Springer Nature, 2024, pp. 485–541, doi:<a href="https://doi.org/10.1007/s00440-023-01254-0">10.1007/s00440-023-01254-0</a>. Clozeau N, Mattesini F. Annealed quantitative estimates for the quadratic 2D-discrete random matching problem. <i>Probability Theory and Related Fields</i>. 2024;190:485-541. doi:<a href="https://doi.org/10.1007/s00440-023-01254-0">10.1007/s00440-023-01254-0</a> Clozeau, Nicolas, and Francesco Mattesini. “Annealed Quantitative Estimates for the Quadratic 2D-Discrete Random Matching Problem.” <i>Probability Theory and Related Fields</i>. Springer Nature, 2024. <a href="https://doi.org/10.1007/s00440-023-01254-0">https://doi.org/10.1007/s00440-023-01254-0</a>. 147972024-01-14T23:00:57Z2025-09-04T11:43:43Z