Recent Progress in the Central Limit Theorem Workshop

22 June 2016, 12.00 PM - 22 June 2016, 5.30 PM

The M Shed, Princes Wharf, Wapping Road, Bristol, BS1 4RN

The Applied Probability section of the Royal Statistical Society announces an afternoon workshop on the Central Limit Theorem. The Central Limit Theorem is one of the cornerstones of probability and statistics, and finds applications in a number of disciplines including number theory, random matrix theory and mathematical physics. This workshop will have four talks on recent results, both from the viewpoint of theoretical methods to prove convergence, and in terms of application areas. 

Speakers

Friedrich Götze - Central Limit Theorem and Expansions: Spectral Statistics and Renyi Entropy Distance.

Abstract: We prove the Central Limit Theoremfor linear statistics of the singular values of a product of two n times n Wigner random matrices for growing dimension n. This is joint work with A. Naumov and A. Tikhomirov. Furthermore, we derive expansions of the Renyi entropy distance ( of index 2 ) of sums of i.i.d. variables to normal laws under almost optimal conditions. This is recent joint work with S. Bobkov and G. Chistyakov.

Giovanni Peccati - Non-Universal second order behaviour of the nodal sets generated by arithmetic random waves.

Abstract: First studied by Rudnick and Wigman, arithmetic random waves are Gaussian Laplace eigenfunctions on the two-dimensional torus. In this talk, I will describe the asymptotic behaviour of the so-called "nodal length" (that, is the volume of the zero set) of such random objects, and show that (quite unexpectedly) it is non-central and non-universal. The non-central behaviour can be understood in terms of an underlying four-dimensional quantitative central limit theorem, and has to be studied by means of highly non-trivial arithmetic considerations. Our approach allows one to explain from a spectral standpoint the so-called "Berry cancellation phenomenon", according to which geometric quantities related to the zeros of random waves have typically smaller fluctuations than those associated with non-zero level sets. Joint work with D. Marinucci (Rome Tor Vergata), M. Rossi (Luxembourg) and I. Wigman (King's College)

Irina Shevtsova - On the accuracy of the normal approximation to sums of independent random variables.

Abstract: New moment-type estimates for the accuracy of the normal approximation to distributions of sums of independent random variables possessing at most three finite moments are presented. The problem of asymptotically exact constants is discussed, and their two-sided bounds and/or exact values are given. The posed problems are considered in various metrics including the uniform (Kolmogorov), the mean and the zeta ones.

Christopher Hughes - The Central Limit Theorem, and beyond, in number theory.

Abstract: The central limit theorem (and other results that look like a CLT but aren't) turn up in many places in number theory. This talk will survey some classical results on the distribution of the values of the Riemann zeta function, and include some new results on the distribution of the zeros of the Riemann zeta function. I will assume no prior knowledge of the Riemann zeta function.

Registration

To register for this workshop please complete the Registration Form.

This workshop has a £25 registration fee. If you are a PhD student, Heilbronn Fellow or RSS member you are able to attend this workshop free of charge. Additionally, we are offering free registration to the first 10 members of Bristol staff to complete the registration form.

Registration fees can be paid via the online shop.

This event is supported by the Heilbronn Institute and EPSRC.

Contact information

For more information regarding the workshop please contact Olly Johnson or Gesine Reinert.

For practical information please contact maths-conference-administrator@bristol.ac.uk

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