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 chosen independently and according to a geometric distribution, and further suppose that is monotonically decreasing. Then for some real . I have been thinking [...]
Posts Tagged ‘partition functions’
A little more about zeta functions and statistical mechanics
Posted in number theory, probability, statistical mechanics, tagged partition functions, zeta functions on November 14, 2010 | 1 Comment »
Zeta functions, statistical mechanics and Haar measure
Posted in group theory, measure theory, number theory, probability, statistical mechanics, tagged compactness, partition functions, profinite groups, q-analogues, universal properties, zeta functions on November 9, 2010 | 3 Comments »
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 write this number is , where is the Riemann zeta function. A few weeks ago this result came up on math.SE in the [...]
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