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  • 1
    Digitale Medien
    Digitale Medien
    The drift of a one-dimensional self-repellent random walk with bounded increments (1994)
    Springer
    Probability theory and related fields 100 (1994), S. 513-544 
    Details
    ISSN: 1432-2064
    Schlagwort(e): 60K35 ; 58E30 ; 60F10 ; 60J15
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary Consider a one-dimensional walk (S k ) k having steps of bounded size, and weight the probability of the path with some factor 1−α∈(0,1) for every single self-intersection up to timen. We prove thatS n /S S converges towards some deterministic number called the effective drift of the self-repellent walk. Furthermore, this drift is shown to tend to the basic drift as α tends to 0 and, as α tends to 1, to the self-avoiding walk's drift which is introduced in [10]. The main tool of the present paper is a representation of the sequence of the local times as a functional of a certain Markov process.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01268992
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  • 2
    Digitale Medien
    Digitale Medien
    The drift of a one-dimensional self-avoiding random walk (1993)
    Springer
    Probability theory and related fields 96 (1993), S. 521-543 
    Details
    ISSN: 1432-2064
    Schlagwort(e): 60K35 ; 58E30 ; 60F10 ; 60J15
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary We prove that a self-avoiding random walk on the integers with bounded increments grows linearly. We characterize its drift in terms of the Frobenius eigenvalue of a certain one parameter family of primitive matrices. As an important tool, we express the local times as a two-block functional of a certain Markov chain, which is of independent interest.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01200208
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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