COOKIES: By using this website you agree that we can place Google Analytics Cookies on your device for performance monitoring. |

University of Cambridge > Talks.cam > Probability > Ordering random variables and racing prime numbers

## Ordering random variables and racing prime numbersAdd to your list(s) Download to your calendar using vCal - Adam Harper (Cambridge)
- Tuesday 16 February 2016, 16:30-17:30
- MR12, CMS, Wilberforce Road, Cambridge, CB3 0WB.
If you have a question about this talk, please contact Perla Sousi. The ``prime number race’’ is the competition between different coprime residue classes mod $q$ to contain the most primes, up to a point $x$. Rubinstein and Sarnak showed, assuming two number theory conjectures, that as $x$ varies the problem is equivalent to a problem about orderings of approximately Gaussian random variables, having weak correlations coming from number theory. In particular, as $q \rightarrow \infty$ the number of primes in any fixed set of $r$ coprime classes will achieve any given ordering for $\sim 1/r!$ values of $x$. I will try to explain what happens when $r$ is allowed to grow as a function of $q$. It turns out that one still sees uniformity of orderings in many situations, but not always. The proofs involve various probabilistic ideas, and also some harmonic analysis related to the Hardy—Littlewood method. This is joint work with Youness Lamzouri. This talk is part of the Probability series. ## This talk is included in these lists:- All CMS events
- All Talks (aka the CURE list)
- CMS Events
- DPMMS Lists
- DPMMS info aggregator
- DPMMS lists
- MR12, CMS, Wilberforce Road, Cambridge, CB3 0WB
- Probability
- School of Physical Sciences
- Statistical Laboratory info aggregator
Note that ex-directory lists are not shown. |
## Other listsActive Materials Martin Centre Research Seminar Series – 44th Annual Series of Lunchtime Lectures Faculty of Music - Lectures## Other talksWorkshop: Holodomor between History and Memory Southern Africa; Northern Cape Uncertainties and Modelling in the Management of Coronary Heart Disease Zoo and Wildlife Work TBC Image Analysis Tools |