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14 relations: Almost surely, Borel–Cantelli lemma, Chebyshev's inequality, Contact process (mathematics), Duality (mathematics), Ergodic process, Interacting particle system, Invariant measure, Markov chain, Probability, Random walk, Sequential dynamical system, Stochastic cellular automaton, Thomas M. Liggett.
Almost surely
In probability theory, one says that an event happens almost surely (sometimes abbreviated as a.s.) if it happens with probability one.
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Borel–Cantelli lemma
In probability theory, the Borel–Cantelli lemma is a theorem about sequences of events.
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Chebyshev's inequality
In probability theory, Chebyshev's inequality (also spelled as Tchebysheff's inequality, Нера́венство Чебышёва, also called Bienaymé-Chebyshev inequality) guarantees that, for a wide class of probability distributions, no more than a certain fraction of values can be more than a certain distance from the mean.
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Contact process (mathematics)
The contact process is a model of an interacting particle system.
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Duality (mathematics)
In mathematics, a duality, generally speaking, translates concepts, theorems or mathematical structures into other concepts, theorems or structures, in a one-to-one fashion, often (but not always) by means of an involution operation: if the dual of A is B, then the dual of B is A. Such involutions sometimes have fixed points, so that the dual of A is A itself.
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Ergodic process
In econometrics and signal processing, a stochastic process is said to be ergodic if its statistical properties can be deduced from a single, sufficiently long, random sample of the process.
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Interacting particle system
In probability theory, an interacting particle system (IPS) is a stochastic process (X(t))_ on some configuration space \Omega.
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Invariant measure
In mathematics, an invariant measure is a measure that is preserved by some function.
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Markov chain
A Markov chain is "a stochastic model describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event".
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Probability
Probability is the measure of the likelihood that an event will occur.
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Random walk
A random walk is a mathematical object, known as a stochastic or random process, that describes a path that consists of a succession of random steps on some mathematical space such as the integers.
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Sequential dynamical system
Sequential dynamical systems (SDSs) are a class of graph dynamical systems.
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Stochastic cellular automaton
Stochastic cellular automata or 'probabilistic cellular automata' (PCA) or 'random cellular automata' or locally interacting Markov chains are an important extension of cellular automaton.
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Thomas M. Liggett
Thomas Milton Liggett (born March 29, 1944) is a mathematician at the University of California, Los Angeles.
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