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  • 1
    Electronic Resource
    Electronic Resource
    Density of states of random Schrödinger operators with a uniform magnetic field (1992)
    Springer
    Letters in mathematical physics 24 (1992), S. 307-321 
    Details
    ISSN: 1573-0530
    Keywords: 05C50 ; 28C20 ; 81S40
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We consider the density of states of Schrödinger operators with a uniform magnetic field and a random potential with a Gaussian distribution. We show that the restriction to the states of the first Landau level is equivalent to a scaling limit where one looks at the density of states near to the energy of the first Landau level and simultaneously lets the strength of the coupling to the random potential go to zero. We also consider a different limit where we look at the suitably normalised density of states near to the energy of the first Landau level when the intensity of the magnetic field goes to infinity.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00420490
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Polymers and random graphs (1991)
    Springer
    Journal of statistical physics 64 (1991), S. 87-110 
    Details
    ISSN: 1572-9613
    Keywords: Gelation of polymers ; giant component of random graph ; grouping of states in a Markov chain ; Erdös-Rényi theorem
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We establish a precise connection between gelation of polymers in Lushnikov's model and the emergence of the giant component in random graph theory. This is achieved by defining a modified version of the Erdös-Rényi process; when contracting to a polymer state space, this process becomes a discrete-time Markov chain embedded in Lushnikov's process. The asymptotic distribution of the number of transitions in Lushnikov's model is studied. A criterion for a general Markov chain to retain the Markov property under the grouping of states is derived. We obtain a noncombinatorial proof of a theorem of Erdös-Rényi type.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01057869
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
    Fulltext
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