The height of watermelons with wall
نویسندگان
چکیده
منابع مشابه
The 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...
متن کاملThe height of watermelons with wall Extended
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...
متن کاملThe height of watermelons with wall 473 � � �
We derive asymptotics for the moments of the height distribution of watermelons with p branches with wall. This generalises a famous result by de Bruijn, Knuth and Rice [2] on the average height of planted plane trees, and a result by Fulmek [6] on the average height of watermelons with two branches.
متن کاملThe height and range of watermelons without wall ( extended abstract )
We determine the weak limit of the distribution of the random variables “height” and “range” on the set of p-watermelons without wall restriction as the number of steps tends to infinity. Additionally, we provide asymptotics for the moments of the random variable “height”.
متن کاملThe Height and Range of Watermelons without Wall
This short note adds some results in parallel to those given in [1] on the random variable height on the set of watermelons with wall. In this paper we prove weak convergence results for the random variables “height” and “range” on the set of watermelons without wall restriction, as well as asymptotics for the moments of the random variable height. The techniques applied are quite similar to th...
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ژورنال
عنوان ژورنال: Journal of Physics A: Mathematical and Theoretical
سال: 2012
ISSN: 1751-8113,1751-8121
DOI: 10.1088/1751-8113/45/9/095003