I’m pretty sure it’s not a requirement that the distribution is uniform and also not path-dependent as per the example I gave - a random walk where you’re not allowed to visit a node more than once.
I’m pretty sure it’s not a requirement that the distribution is uniform and also not path-dependent as per the example I gave - a random walk where you’re not allowed to visit a node more than once.
Here's a reference for the definition I'm using:
https://www.cs.yale.edu/homes/spielman/561/lect10-18.pdf
It's from lecture notes (pdf) from a course in Spectral Graph Theory by Professor Daniel Spielman at Yale.
Those notes look interesting thanks. I’ve really never heard of someone saying you have to have uniform probability for a random walk on a graph. In fact the context where I’m most familiar with them (lattice/grid pricers) it’s always specified something like “the probability of branch a is p and b is 1-p” (ie explicitly not uniform) and they aren’t a weighted graph in the normal sense.
It doesn't have to be uniform or memory less.
However, in general when people mention random walks without further qualifications they are usually talking about the uniform and memoryless case.
That vanilla case can be generalized extensively, on kinds of state spaces, kinds of index sets, kinds of dependence and so on.
That makes sense. THanks.