Timeline for Is there a natural random process that is rigorously known to produce Zipf's law?
Current License: CC BY-SA 4.0
20 events
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| Jan 25 at 22:21 | history | edited | Michael Hardy | CC BY-SA 4.0 |
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| Jul 19, 2014 at 8:03 | comment | added | XL _At_Here_There | Is there any linkage between this question and research on Riemann Hypothesis? | |
| Jan 23, 2014 at 19:25 | answer | added | S Palmer | timeline score: 6 | |
| Jan 25, 2013 at 14:55 | comment | added | Steve Huntsman | arxiv.org/abs/1301.0427 | |
| Jan 18, 2011 at 22:37 | comment | added | user12302 | I wonder if there is a Zipf's Law equivalent of the Glivenko-Cantelli Theorem, where the condition of independence is replaced by requiring a sum of powers remain fixed, and the identical assumption is replaced by a marginal identical assumption? If $C=\sum_{i=1}^n X_i^\alpha$ and $X_i \sim P(X) $ then $\lim_{n \rightarrow \infty} \frac{1}{n} \sum_{i=1}^{n} I(X_i \leq x) \propto \ln(x)$ almost surely? I ask this because empirically Zipf's Law seems to occur when the sample violates independence, and is usually constrained by requiring a fixed sum (like fixed population size, wealth, or resourc | |
| Nov 23, 2010 at 14:17 | answer | added | anon | timeline score: 5 | |
| Sep 21, 2010 at 15:45 | vote | accept | Terry Tao | ||
| Sep 21, 2010 at 14:17 | history | edited | Louigi Addario-Berry |
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| Sep 21, 2010 at 14:17 | history | edited | Louigi Addario-Berry |
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| Sep 21, 2010 at 0:19 | comment | added | Michael Hardy | Good question. It's been a while since I've looked at Zipf's book and I vaguely seem to recall that it was about a large number of different subjects, but maybe I was just missing his point. But I seem to recall that he found that word frequencies in English follow Zipf's law out to about the thousandth word and then suddenly drop off faster. I think the same maybe apply to numbers of postings by usenet posters. | |
| Sep 20, 2010 at 23:09 | answer | added | James Martin | timeline score: 17 | |
| Sep 19, 2010 at 16:38 | answer | added | Alex Chinco | timeline score: 3 | |
| Sep 19, 2010 at 11:43 | answer | added | Pietro Majer | timeline score: 2 | |
| Sep 19, 2010 at 10:28 | answer | added | Manjunath Krishnapur | timeline score: 16 | |
| Sep 19, 2010 at 7:34 | comment | added | Suvrit | Sorry, this is supposed to be comment (but with reputation < 50, one cannot comment). Anyone care to enlighten whether the Pitman-Yor process is a "natural" process to explain Zipf's law (because it is useful for modeling data with power-law tails) | |
| Sep 18, 2010 at 19:39 | comment | added | dorkusmonkey | "From gene families and genera to incomes and internet file sizes: Why power laws are so common in nature":llacolen.ciencias.uchile.cl/~vmunoz/download/papers/rh02.pdf taken from Brian Hayes's article "Fat Tails": americanscientist.org/issues/pub/fat-tails. Not sure if this gives ways of generating Zipf's law with exponent 1, but maybe a random variable with exponential increasing value coupled with an exponentially decreasing probability capped for a particular N? | |
| Sep 18, 2010 at 18:59 | answer | added | Steve Huntsman | timeline score: 19 | |
| Sep 18, 2010 at 18:09 | answer | added | Dick Palais | timeline score: 45 | |
| Sep 18, 2010 at 17:59 | comment | added | gowers | There's a paper called Zipf's Law for Cities: An Explanation with the following abstract. Zipf's law is a very tight constraint on the class of admissible models of local growth. It says that for most countries the size distribution of cities strikingly fits a power law: the number of cities with populations greater than S is proportional to 1/S. Suppose that, at least in the upper tail, all cities follow some proportional growth process (this appears to be verified empirically). This automatically leads their distribution to converge to Zipf's law. I can't access the paper itself though. | |
| Sep 18, 2010 at 16:24 | history | asked | Terry Tao | CC BY-SA 2.5 |