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Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory.

3 votes

The time to drift a binary string from one state to another via deterministic selection of t...

Ignoring the specific binary string structure of the problem for a moment, let's generalize it to an arbitrary digraph $G$ with vertices $V$ and edges $E$ divided into two disjoint subsets $E = E_\mat …
Ilmari Karonen's user avatar
5 votes

What does it mean when we say we have computed a number to a certain accuracy using a probab...

It means pretty much the same thing as when we say that we have measured a physical property to a certain accuracy. That is, in loose terms, it means that we are reasonably certain that the correct v …
Ilmari Karonen's user avatar
9 votes
Accepted

Generalization of a mind-boggling box-opening puzzle

Anna opens the boxes in row-wise, that is, in the order: $1,2,3,4,5,6$. Bert opens the boxes column-wise: $1,4,2,5,3,6$. In the $15$ ways to distribute the two presents into the $6$ boxes, Anna finds …
Ilmari Karonen's user avatar