Topic
Randomness
About: Randomness is a research topic. Over the lifetime, 10725 publications have been published within this topic receiving 252954 citations.
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TL;DR: In this article, it was shown that when the order parameter has a continuous symmetry, the ordered state is unstable against an arbitrarily weak random field in less than four dimensions and the borderline dimensionality above which mean-field-theory results hold is six.
Abstract: Phase transitions are considered in systems where the field conjugate to the order parameter is static and random. It is demonstrated that when the order parameter has a continuous symmetry, the ordered state is unstable against an arbitrarily weak random field in less than four dimensions. The borderline dimensionality above which mean-field-theory results hold is six. (auth)
1,911 citations
04 Oct 2019
TL;DR: A constructive theory of randomness for functions, based on computational complexity, is developed, and a pseudorandom function generator is presented that has applications in cryptography, random constructions, and complexity theory.
Abstract: A constructive theory of randomness for functions, based on computational complexity, is developed, and a pseudorandom function generator is presented. This generator is a deterministic polynomial-time algorithm that transforms pairs (g, r), where g is any one-way function and r is a random k-bit string, to polynomial-time computable functionsf,: { 1, . . . , 2') + { 1, . . . , 2kl. Thesef,'s cannot be distinguished from random functions by any probabilistic polynomial-time algorithm that asks and receives the value of a function at arguments of its choice. The result has applications in cryptography, random constructions, and complexity theory. Categories and Subject Descriptors: F.0 (Theory of Computation): General; F. 1.1 (Computation by Abstract Devices): Models of Computation-computability theory; G.0 (Mathematics of Computing): General; G.3 (Mathematics of Computing): Probability and Statistics-probabilistic algorithms; random number generation
1,679 citations
1,629 citations
TL;DR: As the first part of a study of problems involving common randomness at distance locations, information-theoretic models of secret sharing (generating a common random key at two terminals, without letting an eavesdropper obtain information about this key) are considered.
Abstract: As the first part of a study of problems involving common randomness at distance locations, information-theoretic models of secret sharing (generating a common random key at two terminals, without letting an eavesdropper obtain information about this key) are considered. The concept of key-capacity is defined. Single-letter formulas of key-capacity are obtained for several models, and bounds to key-capacity are derived for other models. >
1,471 citations
Book•
01 Nov 1999
TL;DR: Basic Concept of Reliability, Commonly Used Probability Distributions, and Determination of Distributions and Parameters from Observed Data.
Abstract: Basic Concept of Reliability. Mathematics of Probability. Modeling of Uncertainty. Commonly Used Probability Distributions. Determination of Distributions and Parameters from Observed Data. Randomness in Response Variables. Fundamentals of Reliability Analysis. Advanced Topics on Reliability Analysis. Simulation Techniques. Appendices. Conversion Factors. References. Index.
1,456 citations