Polyharmonic fields and Liouville quantum gravity measures on tori of arbitrary dimension: From discrete to continuous
Year: 2024
Type: article
Abstract: For an arbitrary dimension , we study: the polyharmonic Gaussian field on the discrete torus , that is the random field whose law on given by where is the Lebesgue measure and is the discrete Laplacian; the associated discrete Liouville quantum gravity (LQG) measure associated with it, that is, the random measure on where is a regularity parameter. As , we prove convergence of the fields to the polyharmonic Gaussian field on the continuous torus , as well as convergence of the random measures to the LQG measure on , for all .
Source: Mathematische Nachrichten
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,300
Awards: G11009315, EXC 2047: Hausdorff Center for Mathematics (HCM), Taming Complexity in Partial Differential Systems, G3087154142, G3361734795, Centre de Mathématiques Henri Lebesgue : fondements, interactions, applications et Formation, G3617462173, G3655418302, G3878859087, G4056237041, G4274133347, Optimal Transport and Stochastic Dynamics, G5759884391, G5968008202, Configuration Spaces over Non-Smooth Spaces, SFB 1060: Die Mathematik der emergenten Effekte, Metric measure spaces and Ricci curvature — analytic, geometric, and probabilistic challenges, G8372877233, G9000340908
OpenAlex ID: W4404761412