Multiscale Coupling and the Maximum of P(ϕ)2 Models on the Torus

Article Article scientifique Article Multiscale Coupling and the Maximum of P(ϕ)2 Models on the Torus eng 2023-10-17 2023-10-17 author Barashkov Nikolay author Gunaratnam Trishen 0000-0001-5227-1169 949216 Section de mathématiques (MATH) author Hofstetter Michael 833-882 10.1007/s00220-023-04850-2 0010-3616 https://link.springer.com/10.1007/s00220-023-04850-2 We establish a coupling between the P(ϕ)2 measure and the Gaussian free field on the two-dimensional unit torus at all spatial scales, quantified by probabilistic regularity estimates on the difference field. Our result includes the well-studied ϕ42 measure. The proof uses an exact correspondence between the Polchinski renormalisation group approach, which is used to define the coupling, and the Boué–Dupuis stochastic control representation for P(ϕ)2. More precisely, we show that the difference field is obtained from a specific minimiser of the variational problem. This allows to transfer regularity estimates for the small-scales of minimisers, obtained using discrete harmonic analysis tools, to the difference field. As an application of the coupling, we prove that the maximum of the P(ϕ)2 field on the discretised torus with mesh-size ϵ > 0 converges in distribution to a randomly shifted Gumbel distribution as ϵ → 0 . Dewey 510 European Commission Quantum Fields and Probability 741487 QFPROBA EU H2020 25 Section de mathématiques 11 false Communications in Mathematical Physics 404 2 dcd1ae1c-fa5d-44e8-ae10-583b5802880f Article (Published version) Public Article_scientifique_from_unpaywall.pdf 736551 application/pdf CC BY-4.0 6ccc50e61ffce7c3ff17097f833c2e566d50dbc71f6d6ae3e435068c27c4e8c5 openAccess Faculté des sciences / Section de mathématiques

Title	Published in	Access level	OA Policy	Year	Views	Downloads

Multiscale Coupling and the Maximum of P(ϕ)₂ Models on the Torus	Communications in Mathematical Physics			2023	44	74

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Gunaratnam, Trishen