Re: General 3-state stochastic matrix (again)

• To: mathgroup at smc.vnet.net
• Subject: [mg58233] Re: General 3-state stochastic matrix (again)
• From: Virgil Stokes <virgil.stokes at neuro.ki.se>
• Date: Fri, 24 Jun 2005 02:49:51 -0400 (EDT)
• References: <200506230929.FAA16127@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Steven M. Christensen wrote:

> Your email has come to me with a lot of non-ascii symbols.
>
>Please resend this in pure ascii so we can understand what it
>is.
>
>Moderator
>
>
>
>
>I have tried to find the limit (as n, the power of the matrix, goes to
>infinity) for the general 3-state stochastic matrix using the following
>code:
>
>
>
>Clear[\116\0612, \116\0613, \116\0621, \116\0623, \116\0631, \116\0632]
>T = {{1 - \116\0612 - \116\0613, \116\0612, \116\0613}, {\116\0621, 1 - \116\0621 - \116\0623, \116\0623}, {\116\0631, \116\0632, 1 - \116\0631 - \116\0632}};
>MatrixForm[T]
>xx = MatrixPower[T, n];
>
>MatrixForm[%]
>TimeUsed[]
>zz = Limit[xx, n -> \142\010\036, Assumptions -> 0 < \116\0612 < 1 &&
>0 < \116\0613 <  1 && 0 < \116\0612 + \116\0613 < 1 && 0 < \116\0621 < 1 &&
>       0 < \116\0623 < 1 && 0 < \116\0621 + \116\0623 <  1 && 0 < \116\0631 < 1
>&& 0 < \116\0632 < 1 && 0 <
>\116\0631 + \116\0632 < 1] // FullSimplify;
>TimeUsed[]
>MatrixForm[zz]
>
>However, it does not find a symbolic solution. I would appreciate it
>greatly if someone else could look at this and see if they are able to
>get a symbolic solution. Warning! this can take considerable CPU time.
>
>Note, for a general 2-state stochastic matrix, the above approach works
>fine.
>
>--Thanks,
>V. Stokes
>
>
>
>
>
>
>
>

[Anybody want to indicate how to avoid the symbols in an email above -
moderator]

I have tried several different copy types from Mathematica and finally
used one that when I sent it to myself looked fine. So on my system
Win2K with Mathematica 5.1 it looks fine in the email that I sent to
myself before posting it to the Mathematica group.

What do you suggest that I do?

--V. Stokes

```

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