Stochastic Matrices in Cosmology

[TRB8985]

Good afternoon all,

I'm taking a linear algebra course this semester, and upon entering the topic of 'Applications of Matrix Operations', my professor has given our class the opportunity to earn some extra credit points by writing a paragraph or two on the application of stochastic matrices in any particular field we like.

I'd really like to find some kind of material on some applications of stochastic matrices in cosmology, but unfortunately a large majority of the content out there is locked out from public access without shelling out a hefty fee to some organization or institute.

Could any professionals out there give just a small handful of examples of these kinds of matrices in cosmology or astrophysics? Or even better, shoot a link or two to some interesting tidbits of info on this topic? It would be very highly appreciated.

Thanks, and enjoy your upcoming weekends!

 

[Chalnoth]

Most cosmology papers have free preprints available at arxiv.org. http://scholar.google.com is also very useful for finding free copies of scientific papers in general, if they exist online.

 

[Orodruin]

I addition to what Chalnoth said, university libraries often subscribe to relevant journals. You may want to check with your university library to see if things that are behind a paywall when you search on your own is available at your university.

 

[Chalnoth]

I addition to what Chalnoth said, university libraries often subscribe to relevant journals. You may want to check with your university library to see if things that are behind a paywall when you search on your own is available at your university.

Or any computer on campus, really.

As for the OP, sorry that I don't have anything more specific to add. I haven't ever encountered stochastic matrices in cosmology.

 

[Garth]

As for the OP, sorry that I don't have anything more specific to add. I haven't ever encountered stochastic matrices in cosmology.

Implications of the Reduction Principle for Cosmological Natural Selection maybe?

When mechanisms of variation themselves vary, they are subject to Feldman’s (1972) evolutionary Reduction Principle that selection favors greater faithfulness of replication. A theorem of Karlin (1982) allows one to generalize this principle beyond biological genetics to the unknown inheritance laws that would operate in CNS. The reduction principle for CNS is illustrated with a general multitype branching process model of universe creation containing competing inheritance laws. The most faithful inheritance law dominates the ensemble of universes. The Reduction Principle thus provides a mechanism to account for high fidelity of inheritance between universes.

the mathematical basis of the Reduction Principle was discovered by Karlin [25] (although he did not realize it) in a fundamental theorem on the interaction between growth and mixing: in a system of objects that (1) are changed from one state to another by some transformation processes, and (2) grow or decay in number depending on their state, then greater mixing produces slower growth or faster decay. To be precise, Karlin’s theorem states:
Theorem 1 (Karlin [25, Theorem 5.2]).
Let M be an irreducible stochastic matrix, and D a diagonal matrix with positive diagonal elements.

etc.

Garth

 

[Chalnoth]

Implications of the Reduction Principle for Cosmological Natural Selection maybe?etc.

Garth

Upon further thought, I do recall seeing this in grad school:
http://arxiv.org/abs/1003.2566

Andy Albrecht is the chair of the cosmology department where I went to grad school, UC Davis.