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  • 1. Baik, J.
    et al.
    Deift, P.
    Johansson, Kurt
    KTH, Superseded Departments, Mathematics.
    On the distribution of the length of the second row of a young diagram under Plancherel measure2000In: Geometric and Functional Analysis, ISSN 1016-443X, E-ISSN 1420-8970, Vol. 10, no 4, p. 702-731Article in journal (Refereed)
  • 2. Bjerklöv, Kristian
    Explicit examples of arbitrarily large analytic ergodic potentials with zero Lyapunov exponent2006In: Geometric and Functional Analysis, ISSN 1016-443X, E-ISSN 1420-8970, Vol. 16, no 6, p. 1183-1200Article in journal (Refereed)
    Abstract [en]

    We give explicit examples of arbitrarily large analytic ergodic potentials for which the Schrodinger equation has zero Lyapunov exponent for certain energies. For one of these energies there is an explicit solution. In the quasi-periodic case we prove that one can have positive Lyapunov exponent on certain regions of the spectrum and zero on other regions. We also show the existence of 1-dependent random potentials with zero Lyapunov exponent.

  • 3. Bär, C.
    et al.
    Dahl, Mattias
    KTH, Superseded Departments, Mathematics.
    Small eigenvalues of the Conformal Laplacian2003In: Geometric and Functional Analysis, ISSN 1016-443X, E-ISSN 1420-8970, Vol. 13, no 3, p. 483-508Article in journal (Refereed)
    Abstract [en]

    We introduce a differential topological invariant for compact differentiable manifolds by counting the small eigenvalues of the Conformal Laplace operator. This invariant vanishes if and only if the manifold has a metric of positive scalar curvature. We show that the invariant does not increase under surgery of codimension at least three and we give lower and upper bounds in terms of the alpha-genus.

  • 4. Gelander, Tsachik
    et al.
    Karlsson, Anders
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Margulis, Gregory A.
    Superrigidity, generalized harmonic maps and uniformly convex spaces2007In: Geometric and Functional Analysis, ISSN 1016-443X, E-ISSN 1420-8970, Vol. 17, no 5, p. 1524-1550Article in journal (Refereed)
    Abstract [en]

    We prove several superrigidity results for isometric actions on Busemann non-positively curved uniformly convex metric spaces. In particular we generalize some recent theorems of N. Monod on uniform and certain non-uniform irreducible lattices in products of locally compact groups, and we give a proof of an unpublished result on commensurability superrigidity due to G.A. Margulis. The proofs rely on certain notions of harmonic maps and the study of their existence, uniqueness, and continuity.

  • 5. Khesin, B.
    et al.
    Lenells, Jonatan
    Baylor University, United States.
    Misiołek, G.
    Preston, S. C.
    Geometry of Diffeomorphism Groups, Complete integrability and Geometric statistics2013In: Geometric and Functional Analysis, ISSN 1016-443X, E-ISSN 1420-8970, Vol. 23, no 1, p. 334-366Article in journal (Refereed)
    Abstract [en]

    We study the geometry of the space of densities Dens(M), which is the quotient space Diff(M)/Diffμ(M) of the diffeomorphism group of a compact manifold M by the subgroup of volume-preserving diffeomorphisms, endowed with a right-invariant homogeneous Sobolev Ḣ1 -metric. We construct an explicit isometry from this space to (a subset of) an infinite-dimensional sphere and show that the associated Euler-Arnold equation is a completely integrable system in any space dimension whose smooth solutions break down in finite time. We also show that the Ḣ1-metric induces the Fisher-Rao metric on the space of probability distributions and its Riemannian distance is the spherical version of the Hellinger distance.

  • 6.
    Kurlberg, Pär
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Ueberschaer, Henrik
    Quantum Ergodicity for Point Scatterers on Arithmetic Tori2014In: Geometric and Functional Analysis, ISSN 1016-443X, E-ISSN 1420-8970, Vol. 24, no 5, p. 1565-1590Article in journal (Refereed)
    Abstract [en]

    We prove an analogue of Shnirelman, Zelditch and Colin de VerdiS- re's quantum ergodicity Theorems in a case where there is no underlying classical ergodicity. The system we consider is the Laplacian with a delta potential on the square torus. There are two types of wave functions: old eigenfunctions of the Laplacian, which are not affected by the scatterer, and new eigenfunctions which have a logarithmic singularity at the position of the scatterer. We prove that a full density subsequence of the new eigenfunctions equidistribute in phase space. Our estimates are uniform with respect to the coupling parameter, in particular the equidistribution holds for both the weak and strong coupling quantizations of the point scatterer.

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