A note on saaty's random indexes

A note on random Bulgarian solitaire

We consider a stochastic variant of the game of Bulgarian solitaire [9]. For the stationary measure of the random Bulgarian solitaire, we prove that most of its mass is concentrated on (roughly) triangular configurations of certain type.

A Note on Random Upper Semicontinuous Functions

This note aims at presenting the most general framework for a class U of random upper semicontinuous functions, namely random elements whose sample paths are upper semicontinuous (u.s.c.) functions, defined on some locally compact, Hausdorff and second countable base space, extending Matheron’s framework for random closed sets. It is shown that while the natural embedding process does not provi...

A NOTE ON RANDOM DENSITIES VIA WAVELETSByBrani

It is a well known fact that any orthonormal basis in L 2 can produce a \random density". If fng is an orthonormal basis and fang is a sequence of random variables such that a 2 n = 1 a.s., then f(x) = jann(x)j 2 is a random density. In this note we deene a random density via orthogonal bases of wavelets and explore some of its basic properties.

A note on random number generation

A Note on Maxima in Random Walks

We give a combinatorial proof that a random walk attains a unique maximum with probability at least 1/2. For closed random walks with uniform step size, we recover Dwass’s count of the number of length ` walks attaining the maximum exactly k times. We also show that the probability that there is both a unique maximum and a unique minimum is asymptotically equal to 1 4 and that the probability t...