Random Walks on the Groups of Upper Triangular Matrices
نویسندگان
چکیده
منابع مشابه
Two Random Walks on Upper Triangular Matrices
We study two random walks on a group of upper triangular matrices. In each case, we give upper bound on the mixing time by using a stopping time technique.
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We present an upper bound O(n2) for the mixing time of a simple random walk on upper triangular matrices. We show that this bound is sharp up to a constant, and find tight bounds on the eigenvalue gap. We conclude by applying our results to indicate that the asymmetric exclusion process on a circle indeed mixes more rapidly than the corresponding symmetric process.
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Verardi’s construction of special groups of prime exponent is generalized, and put into a context that helps to decide isomorphism problems and to determine the full group of automorphisms (or at least the corresponding orbit decomposition). The groups in question may be interpreted as groups of unitriangular matrices over suitable rings. Finiteness is not assumed.
متن کاملNon-additive Lie centralizer of infinite strictly upper triangular matrices
Let $mathcal{F}$ be an field of zero characteristic and $N_{infty}(mathcal{F})$ be the algebra of infinite strictly upper triangular matrices with entries in $mathcal{F}$, and $f:N_{infty}(mathcal{F})rightarrow N_{infty}(mathcal{F})$ be a non-additive Lie centralizer of $N_{infty }(mathcal{F})$; that is, a map satisfying that $f([X,Y])=[f(X),Y]$ for all $X,Yin N_{infty}(mathcal{F})...
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we survey some recent results on cocharacters of upper triangular matrices. in particular, we deal both with ordinary and graded cocharacter sequence; we list the principal combinatorial results; we show di erent tech-niques in order to solve similar problems.
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ژورنال
عنوان ژورنال: The Annals of Probability
سال: 1995
ISSN: 0091-1798
DOI: 10.1214/aop/1176987809