Projects per year
Abstract
We find the scaling limits of a general class of boundary-to-boundary connection probabilities and multiple interfaces in the critical planar FK-Ising model, thus verifying predictions from the physics literature. We also discuss conjectural formulas using Coulomb gas integrals for the corresponding quantities in general critical planar random-cluster models with cluster-weight q∈[1,4). Thus far, proofs for convergence, including ours, rely on discrete complex analysis techniques and are beyond reach for other values of q than the FK-Ising model (q=2). Given the convergence of interfaces, the conjectural formulas for other values of q could be verified similarly with relatively minor technical work. The limit interfaces are variants of SLEκ curves (with κ=16/3 for q=2). Their partition functions, that give the connection probabilities, also satisfy properties predicted for correlation functions in conformal field theory (CFT), expected to describe scaling limits of critical random-cluster models. We verify these properties for all q∈[1,4), thus providing further evidence of the expected CFT description of these models.
Original language | English |
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Pages (from-to) | 281-367 |
Number of pages | 87 |
Journal | Probability Theory and Related Fields |
Volume | 189 |
Issue number | 1-2 |
DOIs | |
Publication status | Published - Jun 2024 |
MoE publication type | A1 Journal article-refereed |
Keywords
- 60J67
- 60K35
- 82B20
- Conformal field theory
- Correlation function
- Crossing probability
- FK-Ising model
- Partition function
- Random-cluster model
- Schramm–Loewner evolution
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ISCoURaGe/ 31.12.27: Interplay of structures in conformal and universal random geometry
Peltola, E. (Principal investigator), Poncini, X. (Project Member), Brummet, L. (Project Member), Hughes, L. (Project Member) & Oikarinen, J. (Project Member)
01/01/2023 → 31/12/2027
Project: EU: Framework programmes funding
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Peltola Eveliina AT-palkka: Satunnaisgeometrian konformi-invarianssi
Peltola, E. (Principal investigator), Abuzaid, O. (Project Member) & Brummet, L. (Project Member)
01/09/2021 → 31/08/2026
Project: Academy of Finland: Other research funding
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First Peltola: Finnish centre of excellence in Randomness and STructures
Peltola, E. (Principal investigator), Roussillon, J. (Project Member), Ryan, K. (Project Member) & Immonen, J. (Project Member)
01/01/2022 → 31/12/2024
Project: Academy of Finland: Other research funding