Free stochastic measures via noncrossing partitions II
نویسندگان
چکیده
منابع مشابه
Free Stochastic Measures via Noncrossing Partitions Ii
Rigorous definitions of all these objects in terms of Riemann sums are given below. These definitions were motivated by [RW97], where corresponding definitions were given for usual Levy processes. There is a number of differences between the classical and the free case. First, the free increments property implies that Stπ = 0 unless π is a noncrossing partition. Second, the point of the analysi...
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Abstract. We consider free multiple stochastic measures in the combinatorial framework of the lattice of all diagonals of an n-dimensional space. In this free case, one can restrict the analysis to only the noncrossing diagonals. We give definitions of what free multiple stochastic measures are, and calculate them for the free Poisson and free compound Poisson processes. We also derive general ...
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A (multi)hypergraph H with vertices in N contains a permutation p = a1a2 . . . ak of 1, 2, . . . , k if one can reduce H by omitting vertices from the edges so that the resulting hypergraph is isomorphic, via an increasing mapping, to Hp = ({i, k + ai} : i = 1, . . . , k). We formulate six conjectures stating that if H has n vertices and does not contain p then the size of H is O(n) and the num...
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Using the bijection between partitions and vacillating tableaux, we establish a correspondence between pairs of noncrossing free Dyck paths of length 2n and noncrossing partitions of [2n + 1] with n + 1 blocks. In terms of the number of up steps at odd positions, we find a characterization of Dyck paths constructed from pairs of noncrossing free Dyck paths by using the Labelle merging algorithm.
متن کاملON k-NONCROSSING PARTITIONS
In this paper we prove a duality between k-noncrossing partitions over [n] = {1, . . . , n} and k-noncrossing braids over [n − 1]. This duality is derived directly via (generalized) vacillating tableaux which are in correspondence to tangled-diagrams [6]. We give a combinatorial interpretation of the bijection in terms of the contraction of arcs of tangled-diagrams. Furthermore it induces by re...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 2002
ISSN: 0030-8730
DOI: 10.2140/pjm.2002.207.13