Difference between revisions of "Random mapping"
From Encyclopedia of Mathematics
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| − | A [[ | + | ''$\sigma$ of a set $X = \{1,2,\ldots,n\}$ into itself'' |
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| + | A [[random variable]] taking values in the set $\Sigma_n$ of all single-valued mappings of $X$ into itself. The random mappings $\sigma$ for which the probability $\mathsf{P}\{\sigma=s\}$ is positive only for one-to-one mappings $s$ are called random permutations of degree (order) $n$. The most thoroughly studied random mappings are those for which $\mathsf{P}\{\sigma=s\} = n^{-n}$ for all $s \in\Sigma_n$. A realization of such a random mapping is the result of a simple random selection from $\Sigma_n$. | ||
====References==== | ====References==== | ||
| − | <table><TR><TD valign="top">[1]</TD> <TD valign="top"> V.F. Kolchin, "Random mappings" , Optim. Software (1986) (Translated from Russian)</TD></TR></table> | + | <table> |
| + | <TR><TD valign="top">[1]</TD> <TD valign="top"> V.F. Kolchin, "Random mappings" , Optim. Software (1986) (Translated from Russian) {{ZBL|0605.60010}}</TD></TR> | ||
| + | </table> | ||
Latest revision as of 17:57, 22 November 2016
$\sigma$ of a set $X = \{1,2,\ldots,n\}$ into itself
A random variable taking values in the set $\Sigma_n$ of all single-valued mappings of $X$ into itself. The random mappings $\sigma$ for which the probability $\mathsf{P}\{\sigma=s\}$ is positive only for one-to-one mappings $s$ are called random permutations of degree (order) $n$. The most thoroughly studied random mappings are those for which $\mathsf{P}\{\sigma=s\} = n^{-n}$ for all $s \in\Sigma_n$. A realization of such a random mapping is the result of a simple random selection from $\Sigma_n$.
References
| [1] | V.F. Kolchin, "Random mappings" , Optim. Software (1986) (Translated from Russian) Zbl 0605.60010 |
How to Cite This Entry:
Random mapping. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Random_mapping&oldid=13832
Random mapping. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Random_mapping&oldid=13832
This article was adapted from an original article by V.F. Kolchin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article