Markov Chain probability steady state

Hi there,

A matrix relates to a random walk on a 3 * 3 grid. The grid has nine sqaures and the particles starts at square 1. The particle can move either horizontally or vertically after each step. It stops when it reaches one of the three corners. e.g (1--> 4--> 5--> 8--> 7) Below is the image of the grid and the probability.

I need help in finding the probability of the particle reaching each of the three corner squares at each time until the probabilties settle to a steady value.

Answer 1

[James Tursa]

Hint: The probability of moving from one state to another state in n steps is P^n