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Walks on graphs and statistical mechanics
I finally learned the solution to a little puzzle that’s been bothering me for awhile. The setup of the puzzle is as follows. Let be a weighted undirected graph, e.g. to each edge is associated a...
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Zeta functions, statistical mechanics and Haar measure
An interesting result that demonstrates, among other things, the ubiquity of in mathematics is that the probability that two random positive integers are relatively prime is . A more revealing way to...
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A little more about zeta functions and statistical mechanics
In the previous post we described the following result characterizing the zeta distribution. Theorem: Let be a probability distribution on . Suppose that the exponents in the prime factorization of are...
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I put up a post over at the StackOverflow blog describing a little of what I’ve been up to this summer. Curiously enough, the Zipf distribution which shows up in that post is the same as the zeta...
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Finite noncommutative probability, the Born rule, and wave function collapse
The previous post on noncommutative probability was too long to leave much room for examples of random algebras. In this post we will describe all finite-dimensional random algebras with faithful...
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Maximum entropy from Bayes’ theorem
The principle of maximum entropy asserts that when trying to determine an unknown probability distribution (for example, the distribution of possible results that occur when you toss a possibly unfair...
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