[R] better way to iterate matrix multiplication?

[Jonathan Knibb]

I'm simulating a Markov process using a vector of proportions. Each 
value in the vector represents the proportion of the population who are 
in a particular state (so the vector sums to 1). I have a square matrix 
of transition probabilities, and for each tick of the Markov clock the 
vector is multiplied by the transition matrix.

To illustrate the sort of thing I mean:

pm <- c(0.5,0.5,0)  # half of cases start in state 1, half in state 2
tm <- matrix(runif(9),nrow=3)  # random transition matrix for illustration
tm <- t(apply(tm,1,function (x) x/sum(x)))  # make its rows sum to 1
total.months = 10
for(month in 1:total.months) {pm <- pm %*% tm}  # slow!
pm  # now contains the proportion of cases in each state after 10 months

My question is: is there a quicker, more R-idiomatic way of doing it, 
avoiding 'for'? I've been trying to use apply() to fill a matrix with 
the vectors, but I can't get this to act iteratively.

Suggestions gratefully received!