Topic
Randomness
About: Randomness is a research topic. Over the lifetime, 10725 publications have been published within this topic receiving 252954 citations.
Papers published on a yearly basis
Papers
More filters
TL;DR: It is shown that the random elements as defined by Kolmogorov possess all conceivable statistical properties of randomness and can equivalently be considered as the elements which withstand a certain universal stochasticity test.
Abstract: Kolmogorov has defined the conditional complexity of an object y when the object x is already given to us as the minimal length of a binary program which by means of x computes y on a certain asymptotically optimal machine. On the basis of this definition he has proposed to consider those elements of a given large finite population to be random whose complexity is maximal. Almost all elements of the population have a complexity which is close to the maximal value. In this paper it is shown that the random elements as defined by Kolmogorov possess all conceivable statistical properties of randomness. They can equivalently be considered as the elements which withstand a certain universal stochasticity test. The definition is extended to infinite binary sequences and it is shown that the non random sequences form a maximal constructive null set. Finally, the Kollektivs introduced by von Alises obtain a definition which seems to satisfy all intuitive requirements.
1,228 citations
TL;DR: It is argued that the current picture of RCP cannot be made mathematically precise and support this conclusion via a molecular dynamics study of hard spheres using the Lubachevsky-Stillinger compression algorithm.
Abstract: Despite its long history, there are many fundamental issues concerning random packings of spheres that remain elusive, including a precise definition of random close packing (RCP). We argue that the current picture of RCP cannot be made mathematically precise and support this conclusion via a molecular dynamics study of hard spheres using the Lubachevsky-Stillinger compression algorithm. We suggest that this impasse can be broken by introducing the new concept of a maximally random jammed state, which can be made precise.
1,223 citations
TL;DR: The dynamics of networks between order and randomness, characteristics of small world networks, and the structure and dynamic of networks mark newman.
Abstract: small worlds the dynamics of networks between order and. download small worlds the dynamics of networks between. small worlds and the dynamics of networks. small world networks oxford handbooks. small worlds the dynamics of networks between order and. small worlds the dynamics of networks between order and. book review small worlds the dynamics of networks. small worlds the dynamics of networks between order and. small worlds the dynamics of networks between order and. networks dynamics and the small world phenomenon. small world networks math insight. grossman oakland edu the american mathematical monthly. small world network. small world networks cs brynmawr edu. characteristics of small world networks. small worlds the dynamics of networks between order and. watts d j 1999 small worlds the dynamics of networks. small worlds the dynamics of networks between order and. ef?cient behavior of small world networks. small worlds the dynamics of networks between order and. the structure and dynamics of networks mark newman. small worlds the dynamics of networks between order and. small worlds the dynamics of networks between order and randomness. small worlds the
1,218 citations
04 Oct 2019
TL;DR: A general algorithmic scheme for constructing polynomial-time deterministic algorithms that stretch a short secret random input into a long sequence of unpredictable pseudo-random bits is presented.
Abstract: Much effort has been devoted in the second half of this century to make precise the notion of Randomness. Let us informally recall one of these definitions due to Kolmogorov []. A sequence of bits A =all a2••.•• at is random if the length of the minimal program outputting A is at least k We remark that the above definition is highly non constructive and rules out the possibility of pseudo random number generators. Also. the length of a program, from a Complexity Theory point of view, is a rather unnatural measure. A more operative definition of Randomness should be pursued in the light of modern Complexity Theory.
1,216 citations
TL;DR: It is contended that the small-world network model displays a normal continuous phase transition with a divergent correlation length as the degree of randomness tends to zero, and a real-space renormalization group transformation is proposed and demonstrated that it is exact in the limit of large system size.
1,202 citations