In class we were introduced to the random walk concept. Elise came up with a concept that:
n= number of steps
m= number of vertices
x= number of open vertices at each steps
Have been Have not been at a place
P(x)= n/m P(1-x) = 1-n/m
x >= 3 creates four mini squares in a pane
P(x=1) = (1- n/m)
P(x=2) = (1- n/m)^2
P(x=3) = (1- n/m)^3
if it is on a vertices a square we get (1- n/m)^0
has n goes to infinity.
Expected values
E(x) = 3 (P(x=3)….)) + 2 (P(x=2)….)+ P(x=1)…..)
random walk 2^n is linear
E(x)^n = approximation # of random walk
