Polyharmonic fields and Liouville quantum gravity measures on tori of arbitrary dimension: From discrete to continuous Dello Schiavo, Lorenzo ; https://orcid.org/0000-0002-9881-6870 Herry, Ronan Kopfer, Eva Sturm, Karl Theodor ddc:510 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.). Wiley 2025 info:eu-repo/semantics/article doc-type:article text http://purl.org/coar/resource_type/c_2df8fbb1 https://research-explorer.ista.ac.at/record/18632 https://research-explorer.ista.ac.at/download/18632/18838 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> eng info:eu-repo/semantics/altIdentifier/doi/10.1002/mana.202400169 info:eu-repo/semantics/altIdentifier/issn/0025-584X info:eu-repo/semantics/altIdentifier/e-issn/1522-2616 info:eu-repo/semantics/altIdentifier/wos/001366948500001 info:eu-repo/semantics/altIdentifier/arxiv/2302.02963 info:eu-repo/semantics/openAccess