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Random subcube model

Index Random subcube model

In statistical mechanics, the random-subcube model (RSM) is an exactly solvable model that reproduces key properties of hard constraint satisfaction problems (CSPs) and optimization problems, such as geometrical organization of solutions, the effects of frozen variables, and the limitations of various algorithms like decimation schemes. [1]

Table of Contents

  1. 10 relations: Binary data, Binomial distribution, Boolean satisfiability problem, Chebyshev's inequality, Constraint satisfaction problem, Hypercube, Markov's inequality, Poisson distribution, Random energy model, Statistical mechanics.

Binary data

Binary data is data whose unit can take on only two possible states.

See Random subcube model and Binary data

Binomial distribution

In probability theory and statistics, the binomial distribution with parameters and is the discrete probability distribution of the number of successes in a sequence of independent experiments, each asking a yes–no question, and each with its own Boolean-valued outcome: success (with probability) or failure (with probability).

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Boolean satisfiability problem

In logic and computer science, the Boolean satisfiability problem (sometimes called propositional satisfiability problem and abbreviated SATISFIABILITY, SAT or B-SAT) is the problem of determining if there exists an interpretation that satisfies a given Boolean formula.

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Chebyshev's inequality

In probability theory, Chebyshev's inequality (also called the Bienaymé–Chebyshev inequality) provides an upper bound on the probability of deviation of a random variable (with finite variance) from its mean.

See Random subcube model and Chebyshev's inequality

Constraint satisfaction problem

Constraint satisfaction problems (CSPs) are mathematical questions defined as a set of objects whose state must satisfy a number of constraints or limitations.

See Random subcube model and Constraint satisfaction problem

Hypercube

In geometry, a hypercube is an ''n''-dimensional analogue of a square and a cube.

See Random subcube model and Hypercube

Markov's inequality

In probability theory, Markov's inequality gives an upper bound on the probability that a non-negative random variable is greater than or equal to some positive constant.

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Poisson distribution

In probability theory and statistics, the Poisson distribution is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time if these events occur with a known constant mean rate and independently of the time since the last event.

See Random subcube model and Poisson distribution

Random energy model

In the statistical physics of disordered systems, the random energy model is a toy model of a system with quenched disorder, such as a spin glass, having a first-order phase transition. Random subcube model and random energy model are statistical mechanics.

See Random subcube model and Random energy model

Statistical mechanics

In physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities.

See Random subcube model and Statistical mechanics

References

[1] https://en.wikipedia.org/wiki/Random_subcube_model