L24.5 N-Step Transition Probabilities

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MIT RES.6-012 Introduction to Probability, Spring 2018
Instructor: Patrick Jaillet

License: Creative Commons BY-NC-SA
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Автор

The n-step transition probability can also be proved by "WARSHALL'S ALGORITHM" (not floyd-warshall). It is a Dynamic programming algorithm that multiples the PATH MATRIX (probability matrix in this case) with itself recursively(n times) to give number of N-step path ( Can be divide-and-Conquered as well to reduce the calculation to Log N).
INTERESTING TRIVIA - If I recall correctly, Warshall's algorithm was also demonstrated by Matt Damon in the cult movie - Good Will Hunting :)

LNJP
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One question, what does that upside-down A represent in the notation?

The upside-down A symbol is the universal quantifier from predicate logic, That's the "forall" (for all) symbol, as seen in Wikipedia

johnhhu
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Can anyone please help me understand the line "You do this for all m square pair of ij".
If m = 3, then how come there are 9 pairs of ij ?

sumitdam