2
votes
1answer
52 views

Lattice Path Spaces.

It is well known that the number of paths from $(0,0)$ to $(n,k)$ in $\mathbb{N^2}$ with the set of steps $\{(1,0),(0,1)\}$ is ${n+k \choose k}$. This is the minimum number of steps needed to get to ...
2
votes
0answers
203 views

Probability distribution of a self avoiding walk

Preliminary: Consider a walk on the lattice $\mathbb{Z}_d$ lattice of length $N$. In a normal random walk, if we let $N$ get large the end position has a probability distribution (PDF) that looks ...