Introduction Icebox watermelons weigh between 6 and 15 pounds (2.7 6.8 kilograms) and are growing in popularity in the United States. Sugar Baby was the first icebox watermelon variety in the United States, and was discovered in a field of picnic watermelon in Oklahoma by M. Harden in 1955 (Wehner and Barrett, 1996). It was not until 1986 that the next icebox watermelon varieties were released ...

It is known that the moments of the maximum value of a one-dimensional conditional Brownian motion, the three-dimensional Bessel bridge with duration 1 started from the origin, are expressed using the Riemann zeta function. We consider a system of two Bessel bridges, in which noncolliding condition is imposed. We show that the moments of the maximum value is then expressed using the double Diri...

Abstract We study the watermelon probabilities in uniform spanning forests on two-dimensional semi-infinite square lattice near either open or closed boundary to which can cannot be rooted, respectively. derive universal power laws describing asymptotic decay of these with distance between reference points growing infinity, as well their non-universal constant prefactors. The obtained exponents...

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...

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 ...

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...

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”.