Change search
Refine search result
1 - 13 of 13
CiteExportLink to result list
Permanent link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Rows per page
  • 5
  • 10
  • 20
  • 50
  • 100
  • 250
Sort
  • Standard (Relevance)
  • Author A-Ö
  • Author Ö-A
  • Title A-Ö
  • Title Ö-A
  • Publication type A-Ö
  • Publication type Ö-A
  • Issued (Oldest first)
  • Issued (Newest first)
  • Created (Oldest first)
  • Created (Newest first)
  • Last updated (Oldest first)
  • Last updated (Newest first)
  • Disputation date (earliest first)
  • Disputation date (latest first)
  • Standard (Relevance)
  • Author A-Ö
  • Author Ö-A
  • Title A-Ö
  • Title Ö-A
  • Publication type A-Ö
  • Publication type Ö-A
  • Issued (Oldest first)
  • Issued (Newest first)
  • Created (Oldest first)
  • Created (Newest first)
  • Last updated (Oldest first)
  • Last updated (Newest first)
  • Disputation date (earliest first)
  • Disputation date (latest first)
Select
The maximal number of hits you can export is 250. When you want to export more records please use the Create feeds function.
  • 1. Chinta, Gautam
    et al.
    Jorgenson, Jay
    Karlsson, Anders
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Zeta functions, heat kernels, and spectral asymptotics on degenerating families of discrete tori2010In: Nagoya mathematical journal, ISSN 0027-7630, E-ISSN 2152-6842, Vol. 198, p. 121-172Article in journal (Refereed)
    Abstract [en]

    By a discrete torus we mean the Cayley graph associated to a finite product of finite cycle groups with the generating set given by choosing a generator for each cyclic factor. In this article we examine the spectral theory of the combinatorial Laplacian for sequences of discrete tori when the orders of the cyclic factors tend to infinity at comparable rates. First, we show that the sequence of heat kernels corresponding to the degenerating family converges, after resealing, to the heat kernel on an associated real torus. We then establish an asymptotic expansion, in the degeneration parameter, of the determinant of the combinatorial Laplacian. The zeta-regularized determinant of the Laplacian of the limiting real torus appears as the constant term in this expansion. On the other hand, using a classical theorem by Kirchhoff, the determinant of the combinatorial Laplacian of a finite graph divided by the number of vertices equals the number of spanning trees, called the complexity, of the graph. As a result, we establish a precise connection between the complexity of the Cayley graphs of finite abelian groups and heights of real tori. It is also known that spectral determinants on discrete tori can be expressed using trigonometric functions and that spectral determinants on real tori can be expressed using modular forms on general linear groups. Another interpretation of our analysis is thus to establish a link between limiting values of certain products of trigonometric functions and modular forms. The heat kernel analysis which we employ uses a careful study of I-Bessel functions. Our methods extend to prove the asymptotic behavior of other spectral invariants through degeneration, such as special values of spectral zeta functions and Epstein-Hurwitz type zeta functions.

  • 2. Foertsch, T.
    et al.
    Karlsson, Anders
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Hilbert metrics and Minkowski norms2005In: Journal of Geometry, ISSN 0047-2468, E-ISSN 1420-8997, Vol. 83, no 1-2, p. 22-31Article in journal (Refereed)
    Abstract [en]

    It is shown that the Hilbert geometry (D,h D ) associated to a bounded convex domain D ⊂ double struck E signn is isometric to a normed vector space (V,∥ ̇ ∥) if and only if D is an open n-simplex. One further result on the asymptotic geometry of Hilbert's metric is obtained with corollaries for the behavior of geodesics. Finally we prove that every geodesic ray in a Hilbert geometry converges to a point of the boundary.

  • 3. 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.

  • 4.
    Karlsson, Anders
    KTH, Superseded Departments, Mathematics.
    Free subgroups of groups with nontrivial Floyd boundary2003In: Communications in Algebra, ISSN 0092-7872, E-ISSN 1532-4125, Vol. 31, no 11, p. 5361-5376Article in journal (Refereed)
    Abstract [en]

    We prove that when a countable group admits a nontrivial Floyd-type boundary, then every nonelementary and metrically proper subgroup contains a noncommutative free subgroup. This generalizes the corresponding well-known results for hyperbolic groups and groups with infinitely many ends. It also shows that no finitely generated amenable group admits a nontrivial boundary of this type. This improves on a theorem by Floyd (Floyd, W. J. (1980). Group completions and limit sets of Kleinian groups. Invent. Math. 57: 205-218) as well as giving an elementary proof of a conjecture stated in that same paper. We also show that if the Floyd boundary of a finitely generated group is nontrivial, then it is a boundary in the sense of Furstenberg and the group acts on it as a convergence group.

  • 5.
    Karlsson, Anders
    KTH, Superseded Departments, Mathematics.
    Linear rate of escape and convergence in direction2004In: Random Walks And Geometry / [ed] Kaimanovich, VA, BERLIN 30: WALTER DE GRUYTER & CO , 2004, p. 459-471Conference paper (Refereed)
    Abstract [en]

    This paper describes some situations when random walks (or related processes) of linear rate of escape converge in direction in various senses. We discuss random walks on isometry groups of fairly general metric spaces, and more specifically, random walks on isometry groups of nonpositive curvature, isometry groups of reflexive Banach spaces, and linear groups preserving a proper cone. We give an alternative proof of the main tool from subadditive ergodic theory and we make a conjecture in this context involving Busemann functions.

  • 6.
    Karlsson, Anders
    KTH, Superseded Departments, Mathematics.
    Non-expanding maps and Busemann functions2001In: Ergodic Theory and Dynamical Systems, ISSN 0143-3857, E-ISSN 1469-4417, Vol. 21, p. 1447-1457Article in journal (Refereed)
    Abstract [en]

    We give stronger versions and alternative simple proofs of some results of Beardon, [Be1] and [Be2]. These results concern contractions of locally compact metric spaces and generalize the theorems of Wolff and Denjoy about the iteration of a holomorphic map of the unit disk. In the case of unbounded orbits, there are two types of statements which can sometimes be proven; first, about invariant horoballs, and second, about the convergence of the iterates to a point on the boundary. A few further remarks of similar type are made concerning certain random products of sernicontractions and also concerning semicontractions of Gromov hyperbolic spaces.

  • 7.
    Karlsson, Anders
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    On the dynamics of isometries2005In: Geometry and Topology, ISSN 1465-3060, E-ISSN 1364-0380, Vol. 9, p. 2359-2394Article in journal (Refereed)
    Abstract [en]

    We provide an analysis of the dynamics of isometries and semicontractions of metric spaces. Certain subsets of the boundary at infinity play a fundamental role and are identified completely for the standard boundaries of CAT( 0) spaces, Gromov hyperbolic spaces, Hilbert geometries, certain pseudoconvex domains, and partially for Thurston's boundary of Teichmuller spaces. We present several rather general results concerning groups of isometries, as well as the proof of other more specific new theorems, for example concerning the existence of free nonabelian subgroups in CAT( 0)-geometry, iteration of holomorphic maps, a metric Furstenberg lemma, random walks on groups, noncompactness of automorphism groups of convex cones, and boundary behaviour of Kobayashi's metric.

  • 8.
    Karlsson, Anders
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Ledrappier, Francois
    Linear drift and Poisson boundary for random walks2007In: Pure and Applied Mathematics Quarterly, ISSN 1558-8599, E-ISSN 1558-8602, Vol. 3, no 4, p. 1027-1036Article in journal (Refereed)
    Abstract [en]

    We consider a nondegenerate random walk on a locally compact group with finite first moment. Then, if there are no nonconstant bounded harmonic functions, all the linear drift comes from a real additive character on the group. As a corollary we obtain a generalization of Varopoulos' theorem that in the case of symmetric random walks, positive linear drift implies the existence of nonconstant bounded harmonic functions. Another consequence is the phenomenon that for some groups (including certain Grigorchuk groups) the drift vanishes for any measure of finite first moment.

  • 9.
    Karlsson, Anders
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Ledrappier, Francois
    Liouville property and the linear drift of Brownian motion2007In: Comptes rendus. Mathematique, ISSN 1631-073X, E-ISSN 1778-3569, Vol. 344, no 11, p. 685-690Article in journal (Refereed)
    Abstract [fr]

    Liouville property and the linear drift of Brownian motion. Let M be a complete connected Riemannian manifold with bounded sectional curvature. Under the assumption that M is a regular covering of a manifold with finite volume, we establish that M is Liouville if, and only if, the linear rate of escape of Brownian motion on M vanishes.

  • 10.
    Karlsson, Anders
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Ledrappier, Francois
    On laws of large numbers for random walks2006In: Annals of Probability, ISSN 0091-1798, E-ISSN 2168-894X, Vol. 34, no 5, p. 1693-1706Article in journal (Refereed)
    Abstract [en]

    We prove a general noncommutative law of large numbers. This applies in particular to random walks on any locally finite homogeneous graph, as well as to Brownian motion on Riemannian manifolds which admit a compact quotient. It also generalizes Oseledec's multiplicative ergodic theorem. In addition, we show that epsilon-shadows of any ballistic random walk with finite moment on any group eventually intersect. Some related results concerning Coxeter groups and mapping class groups are recorded in the last section.

  • 11.
    Karlsson, Anders
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Neuhauser, Markus
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Heat kernels, theta identities, and zeta functions on cyclic groups2006In: Topological and Asymptotic Aspects of Group Theory / [ed] rigorchuk, R; Mihalik, M; Sapir, M; Suik, Z, PROVIDENCE: AMER MATHEMATICAL SOC , 2006, Vol. 394, p. 177-189Conference paper (Refereed)
    Abstract [en]

    We prove a theta relation analogous to the classical Poisson-Jacobi theta inversion formula and deduce two formulas for the associated zeta functions. The proof is based on determinations of the heat kernel on Z and on Z/mZ. The theta identity gives in particular an interesting formula for certain sums of Bessel functions.

  • 12.
    Karlsson, Anders
    et al.
    KTH, Superseded Departments, Mathematics.
    Noskov, G. A.
    Some groups having only elementary actions on metric spaces with hyperbolic boundaries2004In: Geometriae Dedicata, ISSN 0046-5755, E-ISSN 1572-9168, Vol. 104, no 1, p. 119-137Article in journal (Refereed)
    Abstract [en]

    We study isometric actions of certain groups on metric spaces with hyperbolic-type bordifications. The class of groups considered includes SLn(Z), Artin braid groups and mapping class groups of surfaces (except the lower rank ones). We prove that in various ways such actions must be elementary. Most of our results hold for non-locally compact spaces and extend what is known for actions on proper CAT(- 1) and Gromov hyperbolic spaces. We also show that SLn(Z) for ngreater than or equal to3 cannot act on a visibility space X without. xing a point in (X) over bar. Corollaries concern Floyd's group completion, linear actions on strictly convex cones, and metrics on the moduli spaces of compact Riemann surfaces. Some remarks on bounded generation are also included.

  • 13.
    Karlsson, Anders
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Woess, Wolfgang
    The Poisson boundary of lamplighter random walks on trees2007In: Geometriae Dedicata, ISSN 0046-5755, E-ISSN 1572-9168, Vol. 124, no 1, p. 95-107Article in journal (Refereed)
    Abstract [en]

    Let T-q be the homogeneous tree with degree q + 1 >= 3 and F a finitely generated group whose Cayley graph is T-q. The associated lamplighter group is the wreath product L integral F, where L is a finite group. For a large class of random walks on this group, we prove almost sure convergence to a natural geometric boundary. If the probability law governing the random walk has finite first moment, then the probability space formed by this geometric boundary together with the limit distribution of the random walk is proved to be maximal, that is, the Poisson boundary. We also prove that the Dirichlet problem at infinity is solvable for continuous functions on the active part of the boundary, if the lamplighter '' operates at bounded range ''.

1 - 13 of 13
CiteExportLink to result list
Permanent link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf