Fermi · Concept Library · Courses · Books · Problems · Simulations · Math Wiki · High School Fermi › Problems Introduction to Probability · Problem 11.16
Random Walks — Grinstead & Snell
Mathematics — Probability · markov-chains-ergodic
Problem (Crowell) Let P \mathbf{P} P ( I + P + ⋯ + P n − 1 ) ( I − P + W ) = I − P n + n W , (\mathbf{I} + \mathbf{P} + \cdots + \mathbf{P}^{n-1})(\mathbf{I} - \mathbf{P} + \mathbf{W}) = \mathbf{I} - \mathbf{P}^n + n\mathbf{W}, ( I + P + ⋯ + P n − 1 ) ( I − P + W ) = I − P n + n W , I + P + ⋯ + P n − 1 n → W , \frac{\mathbf{I} + \mathbf{P} + \cdots + \mathbf{P}^{n-1}}{n} \to \mathbf{W}, n I + P + ⋯ + P n − 1 → W , n → ∞ n \to \infty n → ∞ Browse the problem library