article published yes Lorenzo Dello Schiavo author ECEBF480-9E4F-11EA-B557-B0823DDC885E0000-0002-9881-6870 Ronan Herry author Eva Kopfer author Karl Theodor Sturm author JaMa department Optimal Transport and Stochastic Dynamics project Taming Complexity in Partial Differential Systems project Configuration Spaces over Non-Smooth Spaces project For an arbitrary dimension (Formula presented.), we study: the polyharmonic Gaussian field (Formula presented.) on the discrete torus (Formula presented.), that is the random field whose law on (Formula presented.) given by (Formula presented.) where (Formula presented.) is the Lebesgue measure and (Formula presented.) is the discrete Laplacian; the associated discrete Liouville quantum gravity (LQG) measure associated with it, that is, the random measure on (Formula presented.) (Formula presented.) where (Formula presented.) is a regularity parameter. As (Formula presented.), we prove convergence of the fields (Formula presented.) to the polyharmonic Gaussian field (Formula presented.) on the continuous torus (Formula presented.), as well as convergence of the random measures (Formula presented.) to the LQG measure (Formula presented.) on (Formula presented.), for all (Formula presented.). https://research-explorer.ista.ac.at/download/18632/18838/2025_MathNachrichten_DelloSchiavo.pdf application/pdfno Wiley2025 eng 0025-584X 1522-2616 2302.02963 00136694850000110.1002/mana.202400169 2981244-281 Dello Schiavo, Lorenzo, Ronan Herry, Eva Kopfer, and Karl Theodor Sturm. “Polyharmonic Fields and Liouville Quantum Gravity Measures on Tori of Arbitrary Dimension: From Discrete to Continuous.” <i>Mathematische Nachrichten</i>. Wiley, 2025. <a href="https://doi.org/10.1002/mana.202400169">https://doi.org/10.1002/mana.202400169</a>. Dello Schiavo, Lorenzo, et al. “Polyharmonic Fields and Liouville Quantum Gravity Measures on Tori of Arbitrary Dimension: From Discrete to Continuous.” <i>Mathematische Nachrichten</i>, vol. 298, no. 1, Wiley, 2025, pp. 244–81, doi:<a href="https://doi.org/10.1002/mana.202400169">10.1002/mana.202400169</a>. Dello Schiavo L, Herry R, Kopfer E, Sturm KT. Polyharmonic fields and Liouville quantum gravity measures on tori of arbitrary dimension: From discrete to continuous. <i>Mathematische Nachrichten</i>. 2025;298(1):244-281. doi:<a href="https://doi.org/10.1002/mana.202400169">10.1002/mana.202400169</a> Dello Schiavo L, Herry R, Kopfer E, Sturm KT. 2025. Polyharmonic fields and Liouville quantum gravity measures on tori of arbitrary dimension: From discrete to continuous. Mathematische Nachrichten. 298(1), 244–281. L. Dello Schiavo, R. Herry, E. Kopfer, and K. T. Sturm, “Polyharmonic fields and Liouville quantum gravity measures on tori of arbitrary dimension: From discrete to continuous,” <i>Mathematische Nachrichten</i>, vol. 298, no. 1. Wiley, pp. 244–281, 2025. L. Dello Schiavo, R. Herry, E. Kopfer, K.T. Sturm, Mathematische Nachrichten 298 (2025) 244–281. Dello Schiavo, L., Herry, R., Kopfer, E., &#38; Sturm, K. T. (2025). Polyharmonic fields and Liouville quantum gravity measures on tori of arbitrary dimension: From discrete to continuous. <i>Mathematische Nachrichten</i>. Wiley. <a href="https://doi.org/10.1002/mana.202400169">https://doi.org/10.1002/mana.202400169</a> 186322024-12-08T23:01:56Z2025-04-14T07:27:49Z