Random Walk Recurrence — Pólya's Theorem

Pólya (1921): a simple random walk on ℤᵈ returns to the origin with probability 1 if d ≤ 2 (recurrent), but with probability < 1 if d ≥ 3 (transient). Simulate multiple walkers and measure empirical return rates.

Settings

Step: 0
Returns (total): 0
Return rate: 0.000
Walkers at origin: 0
Pólya theorem:
1D: P(return)=1
2D: P(return)=1
3D: P(return)≈0.341