[
    {
        "id": "authors:zrj3r-fxg71",
        "collection": "authors",
        "collection_id": "zrj3r-fxg71",
        "cite_using_url": "https://authors.library.caltech.edu/records/zrj3r-fxg71",
        "type": "conference_item",
        "title": "Dimension Dependence of Critical Phenomena in Long-Range Percolation",
        "author": [
            {
                "family_name": "Hutchcroft",
                "given_name": "Tom",
                "orcid": "0000-0003-0061-593X",
                "clpid": "Hutchcroft-Tom"
            }
        ],
        "abstract": "<p>Continuing the legacy of the International Congress of Mathematicians, these proceedings bring together presentations delivered by invited speakers at the 2026 Congress held in Philadelphia. Published in collaboration with the International Mathematical Union and edited by Susan Friedlander and Yuri Tschinkel, these seven volumes highlight significant advances across the full spectrum of mathematical research achieved since the previous Congress. The contents of the ICM 2026 Proceedings are available online with open access. Statistical mechanical systems at and near their points of phase transition are expected to exhibit rich, fractal-like behavior that is independent of the small-scale details of the system but depends strongly on the dimension in which the model is defined. Moreover, many models are conjectured to have an upper critical dimension with important quantitative and qualitative differences between critical behavior at, above, and below the upper critical dimension. For models with long-range interactions, one expects additional transitions between effectively long-range and effectively short-range regimes, with further marginal effects on the boundary of these two regimes, leading to (at least) eight qualitatively distinct forms of critical behavior in total for each given model. We first give a broad overview of these conjectures aimed at a general mathematical audience and then survey the significant recent progress being made towards understanding them in the context of long-range percolation.</p>",
        "doi": "10.1137/25m180679x",
        "publisher": "Society for Industrial and Applied Mathematics",
        "publication": "Proceedings of the International Congress of Mathematicians 2026",
        "publication_date": "2026-07",
        "volume": "5",
        "pages": "462-482"
    }
]