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Introduction
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Coarse graining Alice and Dinah
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Coarse graining part I - Clustering algorithms
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Coarse graining part II - Entropy
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Markov Chains
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Mathematics of coarse grained Markov chains
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Mathematics of Coarse grained Markov Chains: The General Case
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A puzzle: origin of the slippy counter
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Where we are so far
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Cellular Automata: Introduction
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Israeli and Goldenfeld; projection and commuting diagrams
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Networks of Renormalization
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Fixing a projection: From CA’s to Ising
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Introduction to the Ising Model
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Coarse-graining the Lattice
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Inducing Quartets & Commutation Failure
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Finding Fixed Points
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Ising Model Simulations
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Poking the Creature: An Introduction to Group Theory
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Irreversible Computations, Forgetful Computers and the Krohn-Rhodes Theorem
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From Quantum Electrodynamics to Plasma Physics
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The Thermal Physics of Plasma
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How does a particle move the plasma?
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Charge Renormalization and Feedback
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Conclusion: Keeping the things that matter
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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.