Spreading maps (polymorphisms), symmetries of Poisson processes and matching summation

Details Spreading maps (polymorphisms), symmetries of Poisson processes and matching summation Spreading maps (polymorphisms), symmetries of Poisson processes and matching summation

2001-12-20

arxiv.org/abs/math-ph/0112046v1

Physics

Mathematical Physics

16 pages, European school on asymptotic combinatorics (St-Petersburg, July 2001)

Scientific paper

The matrix of a permutation is a partial case of Markov transition matrices. In the same way, a measure preserving bijection of a space A with finite measure is a partial case of Markov transition operators. A Markov transition operator also can be considered as a map (polymorphism) A to A, which spreads points of A into measures on A. In this paper, we discuss R-polymorphisms and $\vee$-polymorphisms, who are analogues of the Markov transition operators for the groups of bijections A to A leaving the measure quasiinvariant; two types of the polymorphisms correspond to the cases, when A has finite and infinite measure respectively. We construct a functor from $\vee$-polymorphisms to R-polymorphisms, it is described in terms of summation of convolution products of measures over matchings of Poisson configurations.

Affiliated with

Also associated with

No associations

Rating

Spreading maps (polymorphisms), symmetries of Poisson processes and matching summation does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Spreading maps (polymorphisms), symmetries of Poisson processes and matching summation, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Spreading maps (polymorphisms), symmetries of Poisson processes and matching summation will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-314926