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    MUKHERJEA, ARUNAVA 1979. Probabilistic Analysis and Related Topics.


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  • Currently known as: Journal of the Australian Mathematical Society Title history
    Journal of the Australian Mathematical Society, Volume 23, Issue 4
  • June 1977, pp. 481-498

Random semigroup acts on a finite set

  • Göran Högnäs (a1)
  • DOI: http://dx.doi.org/10.1017/S1446788700019637
  • Published online: 01 April 2009
Abstract
Abstract

Let X be a finite set and S a semigroup of transformations of X. We investigate the trace on X of a random walk on S. We relate the structure of the trace process, which turns out to be a Markov chain, to that of the random walk. We show, for example, that all periods of the trace process divide the period of the random walk.

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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

J. M. Day and A. D. Wallace (1967), ‘Multiplication induced in the state space of an act’, Math. Sys. Theory 1, 305314.

P. Deussen (1971), Halbgruppen und Automaten (Springer, 1971).

P. Martin-Löf (1965), ‘Probability theory on discrete semigroups’, Z. Wahrscheinlichkeitstheorie 4, 78102.

A. Mukherjea , T. C. Sun and N. A. Tserpes (1973), ‘Random walks on compact semigroups’, Proc. Amer. Math. Soc. 39, 599609.

M. Rosenblatt (1971), Markov Processes. Structure and Asymptotic Behavior (Springer, 1971).

D. Stadtlander (1968), ‘Thread actions’, Duke Math. J. 35, 483490.

T. C. Sun , A. Mukherjea and N. A. Tserpes (1973), ‘On recurrent random walks on semigroups’, Trans. Amer. Math. Soc. 185, 213227.

A. D. Wallace (1957), ‘Retractions in semigroups’, Pac. J. Math. 7, 15131517.

A. D. Wallace (1963), ‘Relative ideals in semigroups. II’, Acta Math. Acad. Sci. Hung. 14, 137148.

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Journal of the Australian Mathematical Society
  • ISSN: 1446-7887
  • EISSN: 1446-8107
  • URL: /core/journals/journal-of-the-australian-mathematical-society
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