Recurrence of Random Walks on Completely Simple Semigroups
نویسندگان
چکیده
منابع مشابه
On Completely Simple Semigroups
In this paper completely simple semigroups or generalized groups are considered. We characterize generalized groups which are normal generalized groups. Homomorphisms of generalized groups are considered. Equivalent conditions for the kernel of a homomorphism are deduced. We prove that the group components of a generalized group have the same cardinality. We also prove that if G is a finite nor...
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A formula for the rank of an arbitrary finite completely 0-simple semigroup, represented as a Rees matrix semigroup M[G; I,Λ;P ] , is given. The result generalises that of Ruškuc concerning the rank of connected finite completely 0-simple semigroups. The rank is expressed in terms of |I| , |Λ| , the number of connected components k of P and a number rmin which we define. We go on to show that t...
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We define random walks on Rd and recurrent points and demonstrate that a random walk’s recurrence to 0 implies its recurrence to each of its possible points. We then prove two different necessary and sufficient conditions for the recurrence of random walks. Finally, we employ these results to provide conditions under which random walks on R and on R2 are recurrent as well as prove that when d ≥...
متن کاملHyperbolic Groups and Completely Simple Semigroups
We begin with a brief introduction to the theory of word hyperbolic groups. We then consider four possible conditions which might reasonably be used as definitions or partial definitions of hyperbolicity in semigroups: having a hyperbolic Cayley graph; having hyperbolic Schützenberger graphs; having a context-free multiplication table; or having word hyperbolic maximal subgroups. Our main resul...
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Fountain, Gould and Smith introduced the concept of equivalence of orders in a semigroup and the notion of a maximal order. We examine these ideas in the context of orders in completely 0-simple semigroups with particular emphasis on abundant orders.
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ژورنال
عنوان ژورنال: The Annals of Probability
سال: 1986
ISSN: 0091-1798
DOI: 10.1214/aop/1176992382