A random number generator for continuous random variables

A FORTRAN 4 routine is given which may be used to generate random observations of a continuous real valued random variable. Normal distribution of F(x), X, E(akimas), and E(linear) is presented in tabular form

On a random number of disorders

We register a random sequence which has the following properties: it has three segments being the homogeneous Markov processes. Each segment has his own one step transition probability law and the length of the segment is unknown and random. It means that at two random successive moments (they can be equal also and equal zero too) the source of observations is changed and the first observation in new segment is chosen according to new transition probability starting from the last state of the previous segment. In effect the number of homogeneous segments is random. The transition probabilities of each process are known and a priori distribution of the disorder moments is given. The former research on such problem has been devoted to various questions concerning the distribution changes. The random number of distributional segments creates new problems in solutions with relation to analysis of the model with deterministic number of segments. Two cases are presented in details. In the first one the objectives is to stop on or between the disorder moments while in the second one our objective is to find the strategy which immediately detects the distribution changes. Both problems are reformulated to optimal stopping of the observed sequences. The detailed analysis of the problem is presented to show the form of optimal decision function.disorder problem, sequential detection, optimal stopping, Markov process, change point, double optimal stopping

A recipe for an unpredictable random number generator

In this work we present a model for computation of random processes in digital computers which solves the problem of periodic sequences and hidden errors produced by correlations. We show that systems with non-invertible non-linearities can produce unpredictable sequences of independent random numbers. We illustrate our result with some numerical calculations related with random walks simulations.Comment: 8 pages, 5 figures, Proceedings Mochima spring school in theoretial physic

The t-stability number of a random graph

Given a graph G = (V,E), a vertex subset S is called t-stable (or t-dependent) if the subgraph G[S] induced on S has maximum degree at most t. The t-stability number of G is the maximum order of a t-stable set in G. We investigate the typical values that this parameter takes on a random graph on n vertices and edge probability equal to p. For any fixed 0 < p < 1 and fixed non-negative integer t, we show that, with probability tending to 1 as n grows, the t-stability number takes on at most two values which we identify as functions of t, p and n. The main tool we use is an asymptotic expression for the expected number of t-stable sets of order k. We derive this expression by performing a precise count of the number of graphs on k vertices that have maximum degree at most k. Using the above results, we also obtain asymptotic bounds on the t-improper chromatic number of a random graph (this is the generalisation of the chromatic number, where we partition of the vertex set of the graph into t-stable sets).Comment: 25 pages; v2 has 30 pages and is identical to the journal version apart from formatting and a minor amendment to Lemma 8 (and its proof on p. 21

A Fast and Compact Quantum Random Number Generator

We present the realization of a physical quantum random number generator based on the process of splitting a beam of photons on a beam splitter, a quantum mechanical source of true randomness. By utilizing either a beam splitter or a polarizing beam splitter, single photon detectors and high speed electronics the presented devices are capable of generating a binary random signal with an autocorrelation time of 11.8 ns and a continuous stream of random numbers at a rate of 1 Mbit/s. The randomness of the generated signals and numbers is shown by running a series of tests upon data samples. The devices described in this paper are built into compact housings and are simple to operate.Comment: 23 pages, 6 Figs. To appear in Rev. Sci. Inst