Universal and non-universal large deviations in critical systems
Rare events play a crucial role in understanding complex systems. Characterizing and analyzing them in scale-invariant situations is challenging due to strong correlations. In this work, we focus on characterizing the tails of probability distribution functions (PDFs) for these systems. Using a vari...
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| Format: | Article |
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2025-04-01
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| Series: | SciPost Physics |
| Online Access: | https://scipost.org/SciPostPhys.18.4.119 |
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| author | Ivan Balog, Bertrand Delamotte, Adam Rançon |
| author_facet | Ivan Balog, Bertrand Delamotte, Adam Rançon |
| author_sort | Ivan Balog, Bertrand Delamotte, Adam Rançon |
| collection | DOAJ |
| description | Rare events play a crucial role in understanding complex systems. Characterizing and analyzing them in scale-invariant situations is challenging due to strong correlations. In this work, we focus on characterizing the tails of probability distribution functions (PDFs) for these systems. Using a variety of methods, perturbation theory, functional renormalization group, hierarchical models, large $n$ limit, and Monte Carlo simulations, we investigate universal rare events of critical $O(n)$ systems. Additionally, we explore the crossover from universal to nonuniversal behavior in PDF tails, extending Cramér's series to strongly correlated variables. Our findings highlight the universal and nonuniversal aspects of rare event statistics. We also discuss the ubiquity of this power-law corrections to the leading compressed-exponential decay in these tails in and out-of-equilibrium. |
| format | Article |
| id | doaj-art-4a64ab2b5251466cb5f041ba4794c8d9 |
| institution | DOAJ |
| issn | 2542-4653 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | SciPost |
| record_format | Article |
| series | SciPost Physics |
| spelling | doaj-art-4a64ab2b5251466cb5f041ba4794c8d92025-08-20T03:04:23ZengSciPostSciPost Physics2542-46532025-04-0118411910.21468/SciPostPhys.18.4.119Universal and non-universal large deviations in critical systemsIvan Balog, Bertrand Delamotte, Adam RançonRare events play a crucial role in understanding complex systems. Characterizing and analyzing them in scale-invariant situations is challenging due to strong correlations. In this work, we focus on characterizing the tails of probability distribution functions (PDFs) for these systems. Using a variety of methods, perturbation theory, functional renormalization group, hierarchical models, large $n$ limit, and Monte Carlo simulations, we investigate universal rare events of critical $O(n)$ systems. Additionally, we explore the crossover from universal to nonuniversal behavior in PDF tails, extending Cramér's series to strongly correlated variables. Our findings highlight the universal and nonuniversal aspects of rare event statistics. We also discuss the ubiquity of this power-law corrections to the leading compressed-exponential decay in these tails in and out-of-equilibrium.https://scipost.org/SciPostPhys.18.4.119 |
| spellingShingle | Ivan Balog, Bertrand Delamotte, Adam Rançon Universal and non-universal large deviations in critical systems SciPost Physics |
| title | Universal and non-universal large deviations in critical systems |
| title_full | Universal and non-universal large deviations in critical systems |
| title_fullStr | Universal and non-universal large deviations in critical systems |
| title_full_unstemmed | Universal and non-universal large deviations in critical systems |
| title_short | Universal and non-universal large deviations in critical systems |
| title_sort | universal and non universal large deviations in critical systems |
| url | https://scipost.org/SciPostPhys.18.4.119 |
| work_keys_str_mv | AT ivanbalogbertranddelamotteadamrancon universalandnonuniversallargedeviationsincriticalsystems |