«For dimension ≤ 2, a random walk surely returns to the origin – the walk is recurrent.
For dimension> 2, there is a non-zero probability that the walk never returns – the walk is transient.
Krapivsky et al.2011»
Some years ago one journalist told me: " If a person at each moment of his life has only one or two possibilities, where to work, how to live, then he starts to worry about his life". Due to his experience, each person at each time moment should have at least three possibilities out of each situation, since two possibilities are just the minimal outcome.
But it happens sometimes that people have much more possibilities from each situation, but what does it lead to? Till which time the person will be random walking until he comes to his equilibrium?
The answer to this question for a such complex topology as life's is the following:
Even if at every second a person would have more than two possibilities: to go right or left, then he would never come back to the starting point where he started.