Limit Theorems for the Non-Convex Multispecies Curie–Weiss Model
We study the thermodynamic properties of the generalized non-convex multispecies Curie–Weiss model, where interactions among different types of particles (forming the species) are encoded in a generic matrix. For spins with a generic prior distribution, we compute the thermodynamic limit of the gene...
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2025-04-01
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| author | Francesco Camilli Emanuele Mingione Godwin Osabutey |
| author_facet | Francesco Camilli Emanuele Mingione Godwin Osabutey |
| author_sort | Francesco Camilli |
| collection | DOAJ |
| description | We study the thermodynamic properties of the generalized non-convex multispecies Curie–Weiss model, where interactions among different types of particles (forming the species) are encoded in a generic matrix. For spins with a generic prior distribution, we compute the thermodynamic limit of the generating functional for the moments of the Boltzmann–Gibbs measure using simple interpolation techniques. For Ising spins, we further analyze the fluctuations of the magnetization in the thermodynamic limit under the Boltzmann–Gibbs measure. It is shown that a central limit theorem (CLT) holds for a rescaled and centered vector of species magnetizations, which converges to either a centered or non-centered multivariate normal distribution, depending on the rate of convergence of the relative sizes of the species. |
| format | Article |
| id | doaj-art-db573d677a4e49d7abfba27b79fcf280 |
| institution | DOAJ |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-db573d677a4e49d7abfba27b79fcf2802025-08-20T03:13:45ZengMDPI AGMathematics2227-73902025-04-01138134310.3390/math13081343Limit Theorems for the Non-Convex Multispecies Curie–Weiss ModelFrancesco Camilli0Emanuele Mingione1Godwin Osabutey2Quantitative Life Sciences, International Centre for Theoretical Physics, 34151 Trieste, ItalyDepartment of Matematics, Alma Mater Studiorum, University of Bologna, 40126 Bologna, ItalyDepartment of Matematics, Alma Mater Studiorum, University of Bologna, 40126 Bologna, ItalyWe study the thermodynamic properties of the generalized non-convex multispecies Curie–Weiss model, where interactions among different types of particles (forming the species) are encoded in a generic matrix. For spins with a generic prior distribution, we compute the thermodynamic limit of the generating functional for the moments of the Boltzmann–Gibbs measure using simple interpolation techniques. For Ising spins, we further analyze the fluctuations of the magnetization in the thermodynamic limit under the Boltzmann–Gibbs measure. It is shown that a central limit theorem (CLT) holds for a rescaled and centered vector of species magnetizations, which converges to either a centered or non-centered multivariate normal distribution, depending on the rate of convergence of the relative sizes of the species.https://www.mdpi.com/2227-7390/13/8/1343non-convex Curie–Weiss modelcentral limit theoremIsing modelmultispecies mean-field modelarbitrary spin distribution |
| spellingShingle | Francesco Camilli Emanuele Mingione Godwin Osabutey Limit Theorems for the Non-Convex Multispecies Curie–Weiss Model Mathematics non-convex Curie–Weiss model central limit theorem Ising model multispecies mean-field model arbitrary spin distribution |
| title | Limit Theorems for the Non-Convex Multispecies Curie–Weiss Model |
| title_full | Limit Theorems for the Non-Convex Multispecies Curie–Weiss Model |
| title_fullStr | Limit Theorems for the Non-Convex Multispecies Curie–Weiss Model |
| title_full_unstemmed | Limit Theorems for the Non-Convex Multispecies Curie–Weiss Model |
| title_short | Limit Theorems for the Non-Convex Multispecies Curie–Weiss Model |
| title_sort | limit theorems for the non convex multispecies curie weiss model |
| topic | non-convex Curie–Weiss model central limit theorem Ising model multispecies mean-field model arbitrary spin distribution |
| url | https://www.mdpi.com/2227-7390/13/8/1343 |
| work_keys_str_mv | AT francescocamilli limittheoremsforthenonconvexmultispeciescurieweissmodel AT emanuelemingione limittheoremsforthenonconvexmultispeciescurieweissmodel AT godwinosabutey limittheoremsforthenonconvexmultispeciescurieweissmodel |