help...plz..: random walk problem on 2 D infinite square lattice

Question

souvik · Answer

a particle executing a symmetric random walk on a two dimensional infinite square lattice. find the probability that a particle starting from (0,0) reaches (2,2) in exactly 
i) 6 steps
ii) 7 steps

souvik · Answer

@amistre64

souvik · Answer

n1,n2,n3,n4 be the no of steps to the right, left, up ,down respectively..& r,l,u,d be their probabilities respectively.
N be the no of total steps.
p & q be the net horizontal and vertical displacement..$$\frac{\ N!\ \}\{\ n1\!\ n2\!\ n3\!\ n4\!\ \}\ r \^\{n1\}l \^\{n2\}u \^\{n3\}d \^\{n4\}$$

souvik · Answer

is this right?

souvik · Answer

@Vincent-Lyon.Fr

souvik · Answer

@Michele_Laino

michele_laino · Answer

I'm very sorry, I don't know that answer,  I studied random walk many years ago, and I don't remember it now

souvik · Answer

:( btw can u suggest some books or link so that i can study random walk problem in one and TWO D...........?

michele_laino · Answer

I have studied the random walk in $one$ dimension, using the subsequent textbook:
$$\Large  \begin{gathered}
  {\mathbf{The \; Feynman\; Lecture\; on \;Physics}} \hfill \
  {\text{vol}}{\text{. 1}} \hfill \ 
\end{gathered} $$

amistre64 · Answer

not that i know a solution, but are we able to get from 0,0 to 2,2 in 1 step?  what defines our edges?

souvik · Answer

we have to take 6 or 7 steps...are u talking about boundaries..? there is none as it is infinite lattice..!

amistre64 · Answer

i recall random walks as something in graph theory,  the walk itslef depends on how the vertices are connected, since that is how you get from one point to another
|dw:1447861940138:dw|