Re: [math-fun] reverse-engineering biased Galton boards

you need a precise definition of how to measure "the effect [of] slight perturbations".

a natural definition would be to measure the maximum value of | p_k - P |, where p_k is the probability of passing through (n-k,k-1) and P are all the probabilities of passing through that same point where the individual steps have probability p_{i,j} + - epsilon instead of p_{i,j}. but this seems very hard, and is not likely to give nice results. a slightly different approach: since there are n degrees of freedom here, and the random walk takes n steps, is it possible to make all the p_{i,j} equal if i+j has constant sum (in other words, each step's transition probabilities are independent of the path so far) ? erich