Journal: Probability Theory and Related Fields

Abbreviation

Probab. theory relat. fields

Publisher

Springer

Journal Volumes

ISSN

0178-8051
1432-2064

Description

Filters

Reset filters

Search Results

Publications 1 - 10 of 58
  • Ballisticity conditions for random walk in random environment
    Item type: Journal Article
    Drewitz, Alexander; Ramírez, Alejandro F. (2011)
    Probability Theory and Related Fields
  • On the principal components of sample covariance matrices
    Item type: Journal Article
    Bloemendal, Alex; Knowles, Antti; Yau, Horng-Tzer; et al. (2016)
    Probability Theory and Related Fields
  • Convergence to fractional kinetics for random walks associated with unbounded conductances
    Item type: Journal Article
    Barlow, Martin T.; Černý, Jiří (2011)
    Probability Theory and Related Fields
  • Edge universality for non-Hermitian random matrices
    Item type: Journal Article
    Cipolloni, Giorgio; Erdős, László; Schröder, Dominik (2021)
    Probability Theory and Related Fields
    We consider large non-Hermitian real or complex random matrices X with independent, identically distributed centred entries. We prove that their local eigenvalue statistics near the spectral edge, the unit circle, coincide with those of the Ginibre ensemble, i.e. when the matrix elements of X are Gaussian. This result is the non-Hermitian counterpart of the universality of the Tracy-Widom distribution at the spectral edges of the Wigner ensemble.
  • Covariance estimation with direction dependence accuracy
    Item type: Journal Article
    Abdalla, Pedro; Mendelson, Shahar (2025)
    Probability Theory and Related Fields
    We construct an estimator $\widehatΣ$ for covariance matrices of unknown, centred random vectors X, with the given data consisting of N independent measurements $X_1,...,X_N$ of X and the wanted confidence level. We show under minimal assumptions on X, the estimator performs with the optimal accuracy with respect to the operator norm. In addition, the estimator is also optimal with respect to direction dependence accuracy: $\langle \widehatΣu,u\rangle$ is an optimal estimator for $σ^2(u)=\mathbb{E}\langle X,u\rangle^2$ when $σ^2(u)$ is ``large".
  • Backward SDEs with superquadratic growth
    Item type: Journal Article
    Delbaen, Freddy; Hu, Ying; Bao, Xiaobo (2011)
    Probability Theory and Related Fields
  • On the size of a finite vacant cluster of random interlacements with small intensity
    Item type: Journal Article
    Teixeira, Augusto (2011)
    Probability Theory and Related Fields
  • Dimension transformation formula for conformal maps into the complement of an SLE curve
    Item type: Journal Article
    Gwynne, Ewain; Holden, Nina; Miller, Jason (2020)
    Probability Theory and Related Fields
    We prove a formula relating the Hausdorff dimension of a deterministic Borel subset of R and the Hausdorff dimension of its image under a conformal map from the upper half-plane to a complementary connected component of an SLEκ curve for κ≠4. Our proof is based on the relationship between SLE and Liouville quantum gravity together with the one-dimensional KPZ formula of Rhodes and Vargas (ESAIM Probab Stat 15:358–371, 2011) and the KPZ formula of Gwynne et al. (Ann Probab, 2015). As an intermediate step we prove a KPZ formula which relates the Euclidean dimension of a subset of an SLEκ curve for κ∈(0,4)∪(4,8) and the dimension of the same set with respect to the γ-quantum natural parameterization of the curve induced by an independent Gaussian free field, γ=κ−−√∧(4/κ−−√).
  • A 0-1 law for the massive Gaussian free field
    Item type: Journal Article
    Rodriguez, Pierre-Francois (2017)
    Probability Theory and Related Fields
  • Disconnection, random walks, and random interlacements
    Item type: Journal Article
    Sznitman, Alain-Sol (2017)
    Probability Theory and Related Fields
Publications 1 - 10 of 58