View source for Random mapping

''<img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r077/r077340/r0773401.png" /> of a set <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r077/r077340/r0773402.png" /> into itself''

A [[Random variable|random variable]] taking values in the set <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r077/r077340/r0773403.png" /> of all single-valued mappings of <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r077/r077340/r0773404.png" /> into itself. The random mappings <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r077/r077340/r0773405.png" /> for which the probability <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r077/r077340/r0773406.png" /> is positive only for one-to-one mappings <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r077/r077340/r0773407.png" /> are called random permutations of degree (order) <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r077/r077340/r0773408.png" />. The most thoroughly studied random mappings are those for which <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r077/r077340/r0773409.png" /> for all <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r077/r077340/r07734010.png" />. A realization of such a random mapping is the result of a simple random selection from <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r077/r077340/r07734011.png" />.

====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>