tag:blogger.com,1999:blog-10614348.post544005395463691346..comments2024-01-22T11:26:37.599-08:00Comments on TGD diary: Could one define dynamical homotopy groups in WCW?Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-10614348.post-40514094179289132622015-08-22T16:13:24.548-07:002015-08-22T16:13:24.548-07:00oops, wrong book reference... here is book with th...oops, wrong book reference... here is book with the formula I transliterated<br /><br />https://books.google.com/books?id=xM3PStPHY-sC&pg=PA74&lpg=PA74&dq=%22it+is+unique+aside+from+an+additive+constant+and+a+harmless+ambiguity+at+its+jumps%22&source=bl&ots=kfl99ZVaKa&sig=f0AwhCjhtRDXp-xkiXJ2V85oEXQ&hl=en&sa=X&ved=0CCEQ6AEwAGoVChMI3tD9hui9xwIVzJkeCh1IJg7q#v=onepage&q=%22it%20is%20unique%20aside%20from%20an%20additive%20constant%20and%20a%20harmless%20ambiguity%20at%20its%20jumps%22&f=false<br />Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-10614348.post-21454736980761556232015-08-22T15:22:14.904-07:002015-08-22T15:22:14.904-07:00I meant to post that comment on the other blog pos...I meant to post that comment on the other blog post to this one.. oops, here it is. I read some of the paper.. this is incredible... <br /><br />http://arxiv.org/abs/1503.07851<br /><br />this seems related to 3.8#SpectralFunctions of @Book{bochner1955harmonic,<br /> Title = {Harmonic Analysis and the Theory of Probability},<br /> Author = {Bochner, Solomon},<br /> Publisher = {University of California Press},<br /> Year = {1955},<br /> Series = {California Monographs in mathematical sciences},<br />}<br /><br />or am I getting that confused with something else? I remember thinking it was the appearance of the polynomials and the anti-symmetrization involing the binomial processes and theorem, etc. <br /><br />$\lim_{n \rightarrow \infty} \sum_{j = 1}^n \sum_{k = 1}^n \frac{f_{\gamma}\left( \frac{j}{n} \right) f_{\gamma}^{\ast} \left( \frac{k}{n} \right) Q\left( \frac{j - k}{n} \right)}{n^2} = \lim_{n \rightarrow \infty} E \left|\sum_{j = 1}^n \frac{f_{\gamma} \left( \frac{j}{n} \right) g \left(\frac{j}{n} \right)}{n} \right|^2$<br /><br />see a (much more readable image) at http://i.imgur.com/FhLxAO4.png ;-)<br /><br />--crοw<br />Anonymousnoreply@blogger.com