منابع مشابه
Gaps in Discrete Random Samples
Let (Xi)i∈N be a sequence of independent and identically distributed random variables with values in the set N0 of non-negative integers. Motivated by applications in enumerative combinatorics and analysis of algorithms we investigate the number of gaps and the length of the longest gap in the set {X1, . . . , Xn} of the first n values. We obtain necessary and sufficient conditions in terms of ...
متن کاملGaps in discrete random samples: extended abstract
Motivated by applications in enumerative combinatorics and the analysis of algorithms we investigate the number of gaps and the length of the longest gap in a discrete random sample from a general distribution. We obtain necessary and sufficient conditions on the underlying distribution for the gaps to vanish asymptotically (with probability 1, or in probability), and we study the limiting dist...
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In this note we continue the study of gaps in samples of geometric random variables originated in Hitczenko and Knopfmacher [Gap-free compositions and gap-free samples of geometric random variables. Discrete Math. 294 (2005) 225–239] and continued in Louchard and Prodinger [The number of gaps in sequences of geometrically distributed random variables, Preprint available at 〈http://www.ulb.ac.be...
متن کاملPruned Discrete Random Samples
Let Xi, i ∈ N, be independent and identically distributed random variables with values in N0. We transform (‘prune’) the sequence {X1, . . . , Xn}, n ∈ N, of discrete random samples into a sequence {0, 1, 2, . . . , Yn}, n ∈ N, of contiguous random sets by replacing Xn+1 with Yn + 1 if Xn+1 > Yn. We consider the asymptotic behaviour of Yn as n → ∞. Applications include path growth in digital se...
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It is proved that if the Continuum Hypothesis is true, then one random real always produces a destructible (ω1, ω1) gap.
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ژورنال
عنوان ژورنال: Journal of Applied Probability
سال: 2009
ISSN: 0021-9002,1475-6072
DOI: 10.1017/s0021900200006124