# Complexity Explorer Santa Fe Institute ## Introduction to Renormalization

• Introduction
• Coarse graining Alice and Dinah
• Coarse graining part I - Clustering algorithms
• Coarse graining part II - Entropy
• Markov Chains
• Mathematics of coarse grained Markov chains
• Mathematics of Coarse grained Markov Chains: The General Case
• A puzzle: origin of the slippy counter
• Where we are so far
• Cellular Automata: Introduction
• Israeli and Goldenfeld; projection and commuting diagrams
• Networks of Renormalization
• Coarse-graining the Lattice
• From Quantum Electrodynamics to Plasma Physics
• Conclusion: Keeping the things that matter
• Homework

#### 2.2 Mathematics of coarse grained Markov chains » Quiz Solution

In the slippy counter, with probability ep (epsilon) for remaining in the same state, what's the probability that, if I begin in state A, I end up back in state A after three timesteps?

A. B. C. D. Answer: (A). You can work this out in two ways. The quick way is to multiply the transition matrix against itself three times. The long way is to consider all the possible paths: A->A->A->A (probability ), A->B->A->A (probability ) and so on.