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・ Probabilistic argument
・ Probabilistic argumentation
・ Probabilistic automaton
・ Probabilistic bisimulation
・ Probabilistic causation
・ Probabilistic classification
・ Probabilistic CTL
・ Probabilistic data association filter
・ Probabilistic database
・ Probabilistic design
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Probabilistic method
・ Probabilistic metric space
・ Probabilistic neural network
・ Probabilistic number theory
・ Probabilistic prognosis
・ Probabilistic programming language
・ Probabilistic proposition
・ Probabilistic relevance model
・ Probabilistic risk assessment
・ Probabilistic roadmap
・ Probabilistic soft logic
・ Probabilistic Turing machine
・ Probabilistic voting model
・ Probabilistic-based design optimization
・ Probabilistically checkable proof


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Probabilistic method : ウィキペディア英語版
Probabilistic method

The probabilistic method is a nonconstructive method, primarily used in combinatorics and pioneered by Paul Erdős, for proving the existence of a prescribed kind of mathematical object. It works by showing that if one randomly chooses objects from a specified class, the probability that the result is of the prescribed kind is more than zero. Although the proof uses probability, the final conclusion is determined for ''certain'', without any possible error.
This method has now been applied to other areas of mathematics such as number theory, linear algebra, and real analysis, as well as in computer science (e.g. randomized rounding), and information theory.
==Introduction==
If every object in a collection of objects fails to have a certain property, then the probability that a random object chosen from the collection has that property is zero.
Similarly, showing that the probability is (strictly) less than 1 can be used to prove the existence of an object that does ''not'' satisfy the prescribed properties.
Another way to use the probabilistic method is by calculating the expected value of some random variable. If it can be shown that the random variable can take on a value less than the expected value, this proves that the random variable can also take on some value greater than the expected value.
Common tools used in the probabilistic method include Markov's inequality, the Chernoff bound, and the Lovász local lemma.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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