Journal: Probability and Mathematical Physics

Abbreviation

Publisher

Mathematical Sciences Publishers

Journal Volumes

ISSN

2690-1005
2690-0998

Description

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2020 - 20213
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Publications 1 - 3 of 3
  • Excess deviations for points disconnected by random interlacements
    Item type: Journal Article
    Sznitman, Alain-Sol (2021)
    Probability and Mathematical Physics
  • Optimal lower bound on the least singular value of the shifted Ginibre ensemble
    Item type: Journal Article
    Cipolloni, Giorgio; Erdős, László; Schröder, Dominik (2020)
    Probability and Mathematical Physics
    We consider the least singular value of a large random matrix with real or complex i.i.d. Gaussian entries shifted by a constant z∈C. We prove an optimal lower tail estimate on this singular value in the critical regime where z is around the spectral edge, thus improving the classical bound of Sankar, Spielman and Teng (SIAM J. Matrix Anal. Appl. 28:2 (2006), 446–476) for the particular shift-perturbation in the edge regime. Lacking Brézin–Hikami formulas in the real case, we rely on the superbosonization formula (Comm. Math. Phys. 283:2 (2008), 343–395).
  • Normally hyperbolic trapping on asymptotically stationary spacetimes
    Item type: Journal Article
    Hintz, Peter (2021)
    Probability and Mathematical Physics
    We prove microlocal estimates at the trapped set of asymptotically Kerr spacetimes: these are spacetimes whose metrics decay inverse polynomially in time to a stationary subextremal Kerr metric. This combines two independent results. The first one is purely dynamical: we show that the stable and unstable manifolds of a decaying perturbation of a time-translation-invariant dynamical system with normally hyperbolic trapping are smooth and decay to their stationary counterparts. The second, independent, result provides microlocal estimates for operators whose null-bicharacteristic flow has a normally hyperbolic invariant manifold, under suitable nondegeneracy conditions on the stable and unstable manifolds; this includes operators on closed manifolds, as well as operators on spacetimes for which the invariant manifold lies at future infinity.
Publications 1 - 3 of 3