User quantumbrian - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-25T13:52:32Z http://mathoverflow.net/feeds/user/1970 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/37446/spacing-of-zeros-of-zeta-function-on-the-critical-line/37472#37472 Answer by QuantumBrian for Spacing of zeros of zeta function on the critical line QuantumBrian 2010-09-02T09:10:22Z 2010-09-02T09:10:22Z <p>I believe \$\Lambda(k)\$ is the lower bound that arises from assuming the \$k\$th moment is predicted by random matrix theory (equation (1.13)) with the explicit constants \$b(h,k)\$ derived by Hughes. The method seems to require knowledge of the constants \$b(k,k)\$. Indeed at the top of page 5 he discusses the work of Hall in the case \$h=3\$, for which the value of \$\Lambda\$ derived (equation (1.17)) occurs in the table (1.18) as \$\Lambda(3)\$.</p> http://mathoverflow.net/questions/20817/mathematical-means-of-studying-large-and-complex-but-finite-systems/20821#20821 Answer by QuantumBrian for Mathematical means of studying large and complex but finite systems? QuantumBrian 2010-04-09T08:38:06Z 2010-04-09T08:38:06Z <p>Random Matrix Theory. Wigner originally used random Hermitian matrices to model nuclear resonances in large atomic nucleii. In this way he was able to derive a prediction for the spacings between resonances that agreed with experimental data. Since then random matrix theory has been used to model a large variety of complex systems. A review (from the physics point of view) is at: <a href="http://arxiv.org/abs/cond-mat/9707301" rel="nofollow">http://arxiv.org/abs/cond-mat/9707301</a></p> <p>Mathematically, random matrix theory is a well-developed, rigorous theory. It has been found to have unexpected relations with e.g. number theory, and random permutations. Questions of universality have been studied in recent work by Terence Tao and Van Vu and co-workers.</p> http://mathoverflow.net/questions/6233/order-statistics-for-components-of-a-random-unit-vector/6244#6244 Answer by QuantumBrian for order statistics for components of a random unit vector QuantumBrian 2009-11-20T10:13:47Z 2009-11-20T10:13:47Z <p>There has been some work in the physics community on extreme statistics (i.e. distribution of largest and smallest components) of random vectors. See, <a href="http://arxiv.org/abs/0708.0176/" rel="nofollow" title="ArXiv:0708.0176">link text</a> for example. The largest component is approximately distributed like a Gumbel random variable, while the smallest component is approximately distributed like an exponential random variable.</p> http://mathoverflow.net/questions/44053/why-are-polynomials-easier-to-handle-with-than-integers Comment by QuantumBrian QuantumBrian 2010-10-29T08:36:50Z 2010-10-29T08:36:50Z Long division with polynomials is much easier than long division of integers (do students even learn that any more?). That's also probably due to the &quot;no carry-over&quot; mentioned in Amri's comment.