Singularity Notes

Had read this interesting paper by Michael Mitzenmacher some time ago and always wanted to blog about this. Now is a good time as any, while I wait for a long download to finish. The paper talks about the new found interest in the power-law and log-normal distributions especially among web researchers. Michael provides ample evidence to show that these debates are nothing new. Power-law versus log-normal processes have been debated in several areas like biology, chemistry and astronomy for more than a century now. A power-law distribution over a random variable X is one where the probability that X takes a value at least k is proportional to k -g . Here g > 0 is the power-law "exponent". Intuitively a power-law distribution represents a system where X has a very large number of instances of very small values and a very small number of instances of extremely large values. Power-law distributions are also called scale-free distributions as their overall shape appears the s