Watermelons
نویسندگان
چکیده
منابع مشابه
Stars and Watermelons
Gillet [3] demonstrated that limn→∞Wk(b2n tc)/ √ 2n tends to a family of p nonintersecting Brownian excursions, 0 ≤ t ≤ 1, as an extension of a principle given in [4]. The height of a path Wk in a p-watermelon with wall is the maximum value of Wk(i) over all i. The area under a path Wk is the area of the polygonal region determined by the curve j = Wk(i), the horizontal line j = 0, and the vert...
متن کاملAsymptotic behaviour of watermelons
A watermelon is a set of p Bernoulli paths starting and ending at the same ordinate, that do not intersect. In this paper, we show the convergence in distribution of two sorts of watermelons (with or without wall condition) to processes which generalize the Brownian bridge and the Brownian excursion in Rp. These limit processes are defined by stochastic differential equations. The distributions...
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Watermelons Citrullus lanatus (Thumb.) Mansf. were reported to be growing in Africa, Middle East, Central Asia, Mediterranean Coasts, Europe and America in the late 1500s. Growth spread to Japan from South China and Southeast Asia. Fruits were basic food for people and animals in these countries, however the fruits bore little resemblance to current cultivars in size, shape, color and internal ...
متن کاملThe Height of Watermelons with Wall
Abstract. We derive asymptotics for the moments as well as the weak limit of the height distribution of watermelons with p branches with wall. This generalises a famous result of de Bruijn, Knuth and Rice [4] on the average height of planted plane trees, and results by Fulmek [9] and Katori et al. [14] on the expected value, respectively higher moments, of the height distribution of watermelons...
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The model of vicious walkers was introduced by Fisher [4]. He gave a number of applications in physics, such as modelling wetting and melting processes. In general, the model of vicious walkers is concerned with p random walkers on a d-dimensional lattice. In the lock step model, at each time step all of the walkers move one step in any of the allowed directions, such that at no time any two ra...
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ژورنال
عنوان ژورنال: The Iowa Review
سال: 2006
ISSN: 0021-065X,2330-0361
DOI: 10.17077/0021-065x.6115