Dirichlet Spaces Associated with Locally Finite Rooted Directed Trees
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DOI: 10.1007/s00020-017-2400-z
Abstract: Let $$\mathscr {T}=(V, \mathcal E)$$T=(V,E) be a leafless, locally finite rooted directed tree. We associate with $$\mathscr {T}$$T a one parameter family of Dirichlet spaces $$\mathscr {H}_q~(q \geqslant 1)$$Hq(q⩾1), which turn out to be Hilbert… read more here.
Keywords: directed trees; dirichlet spaces; rooted directed; finite rooted ... See more keywords
Joint distributions of numbers of runs of specified lengths on directed trees
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DOI: 10.1007/s00362-016-0762-y
Abstract: In this paper, we consider exact joint distributions of numbers of success runs of specified lengths on a Markov directed tree under $$\ell $$ℓ-overlapping enumeration schemes. Methods for deriving the probability generating functions of the… read more here.
Keywords: specified lengths; distributions numbers; directed trees; runs specified ... See more keywords