Journal: Duke Mathematical Journal

Abbreviation

Duke Math. J.

Publisher

Duke University Press

Journal Volumes

ISSN

0012-7094
1547-7398

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Publications 1 - 10 of 47
  • Equality of Critical Parameters for Percolation of Gaussian Free Field Level Sets
    Item type: Journal Article
    Duminil-Copin, Hugo; Goswami, Subhajit; Rodriguez, Pierre-François; et al. (2023)
    Duke Mathematical Journal
    We consider upper level sets of the Gaussian free field (GFF) on Zd, for d > 3, above a given real-valued height parameter h. As h varies, this defines a canonical percolation model with strong, algebraically decaying correlations. We prove that three natural critical parameters associated with this model, respectively describ-ing a well-ordered subcritical phase, the emergence of an infinite cluster, and the onset of a local uniqueness regime in the supercritical phase, actually coincide. At the core of our proof lies a new interpolation scheme aimed at integrating out the long-range dependence of the GFF. Due to the strength of correlations, its successful implementation requires that we work in an effectively critical regime. Our analysis relies extensively on certain novel renormalization techniques that bring into play all relevant scales simultaneously. The approach in this article paves the way to a complete understanding of the off-critical phases for strongly correlated disordered systems.
  • Blowup of the BV norm in the multidimensional Keyfitz and Kranzer system
    Item type: Journal Article
    De Lellis, Camillo (2005)
    Duke Mathematical Journal
  • Integration of twisted Dirac brackets
    Item type: Journal Article
    Bursztyn, Henrique; Crainic, Marius; Weinstein, Alan; et al. (2004)
    Duke Mathematical Journal
  • The Frobenius properad is Koszul
    Item type: Journal Article
    Campos, Ricardo; Merkulov, Sergei; Willwacher, Thomas (2016)
    Duke Mathematical Journal
  • The unique tangent cone property for weakly holomorphic maps into projective algebraic varieties
    Item type: Journal Article
    Caniato, Riccardo; Rivière, Tristan (2023)
    Duke Mathematical Journal
    We establish the uniqueness of tangent maps for general weakly holomorphic and locally approximable maps from an arbitrary almost complex manifold into projective algebraic varieties. As a by-product of the approach and the techniques developed, we also obtain the unique tangent cone property for a special class of nonrectifiable positive pseudoholomorphic cycles. This approach also gives a new proof of the main result by Bellettini on the uniqueness of tangent cones for positive integral (p, p)-cycles in arbitrary almost complex manifolds.
  • Supercritical percolation on graphs of polynomial growth
    Item type: Journal Article
    Contreras, Daniel; Martineau, Sébastien; Tassion, Vincent (2024)
    Duke Mathematical Journal
    We consider Bernoulli percolation on transitive graphs of polynomial growth. In the subcritical regime (p < p꜀), it is well known that the connection probabilities decay exponentially fast. In the present paper, we study the supercritical phase (p > p꜀) and prove the exponential decay of the truncated connection probabilities (probabilities that two points are connected by an open path, but not to infinity). This sharpness result was established by Chayes, Chayes, and Newman on Zᵈ and uses the difficult slab result of Grimmett and Marstrand. However, the techniques used there are very specific to the hypercubic lattices and do not extend to more general geometries. In this paper, we develop new robust techniques based on the recent progress in the theory of sharp thresholds and the sprinkling method of Benjamini and Tassion. On Zᵈ, these methods can be used to produce a new proof of the slab result of Grimmett and Marstrand.
  • Global in time measure-valued solutions and finite-time aggregation for nonlocal interaction equations
    Item type: Journal Article
    Carrillo, José A.; DiFrancesco, Marco; Figalli, Alessio; et al. (2011)
    Duke Mathematical Journal
  • Weight 2 compactly supported cohomology of moduli spaces of curves
    Item type: Journal Article
    Payne, Sam; Willwacher, Thomas (2024)
    Duke Mathematical Journal
  • Motivic decomposition of isotropic projective homogeneous varieties
    Item type: Journal Article
    Chernousov, Vladimir; Gille, Stefan; Merkurjev, Alexander (2005)
    Duke Mathematical Journal
  • Two extensions of Ramsey's theorem
    Item type: Journal Article
    Conlon, David; Fox, Jacob; Sudakov, Benny (2013)
    Duke Mathematical Journal
Publications 1 - 10 of 47