I am reading in wikipedia about random permutation and here appear the next term "permutation-valued random variable". Could you give me a book where exist this definition please? Do you have any example?
Asked
Active
Viewed 214 times
0
-
In all likelihood random permutation and permutation valued random variable are the same thing. – Paul Aug 18 '18 at 17:15
-
Random variables are just measurable functions on probability spaces, so a permutation valued random variable is just a measurable map from a probability space to the set of permutations. Likely the sigma algebra on the permutations is the discrete one. – cdipaolo Aug 18 '18 at 17:18
-
@cdipaolo Do you know an example of probability space for a permutation-valued random variable? – juaninf Aug 18 '18 at 20:19
-
@juaninf you could use $X={1,2,\ldots , n!}$ with normalized counting measure, and then a bijection from $X$ to the set of permutations on $n$ elements would give you a uniform distribution on the permutations (a permutation valued random variable!) – cdipaolo Aug 19 '18 at 02:31